abn_structured rate manual

Structured Rates

ManualPrivate Investor Products

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Interest rate linked structured notes, whose payoffsdepend on future interest rates, have been very popularin recent years with Private Investors. The appeal ofstructured products lies in their ability to deliver highlycustomised returns for investors, consistent with theirunique investment objectives.

This manual highlights the range of structured rate productsand intends to provide private wealth managers and theirclients with a selection of different investment opportunities,which enables one to express specific views on any futureinterest rate development. All structures can be in eithernote or swap form.

Included in the manual is a consideration of the investor’sview versus his risk appetite. While structured rate productsare flexible instruments by nature and almost every productcan be structured to suit the investor’s risk appetite, someproducts will appeal more to the conservative investorwhile other products suit investors with a strong view ora more aggressive attitude.

Most notes are sold in principal protected form, wherebyonly the coupon is at risk. It is also possible to generatemore upside potential by structuring the product so that(part of) the notional is at risk. Views on absolute interestrate levels and relative differences between interest ratescan be expressed through interest rate linked structurednotes.

Key Advantages of Structured RateProducts

Highly Customised: Structured rate products are tailoredto fit investors’ unique requirements. They create risk-return profiles that would normally be inaccessible to theprivate investor.

Enhanced Yield: By expressing a view and accepting acertain risk, investors can achieve higher returns on theirinvestments than they would receive with traditionalproducts.

Convenience: The use of structured rate products allowsparticular risk-return payoffs that can be difficult orexpensive to create in the markets available to the investor.

Potential Clients

Private InvestorsAsset ManagersPrivate BanksCorporatesInsurance Companies and Pension Funds

For any additional information regarding structured rateproducts, please contact your local sales representative.

Pieter-Reinier Maat

Head of Financial Market Products

Sven Haefner

Global Head of PIP Products

This Structured Rates Manual ("Manual") is designed to help distributors of financial products identify an investment approach and product range thatcould generally suit their clients. The Manual is intended as a summary only and the information contained therein is not intended to be exhaustive.The information provided is for general consideration only and the Manual in no way constitutes investment advice or a recommendation from ABNAMRO Bank N.V.. Distributors should ensure that investors are fully aware of the risks involved in the purchase of investment products and shouldcomply with all prevailing law. This material is for information purposes only and is not intended as an offer or solicitation with respect to the purchaseor sale of any particular security. Past performance is not a guarantee of future performance. For further disclaimer information please see page 66 of this Manual.

Introduction

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Features (and their most popular variants)Snowball: 29

> Snowball Note (Ladder Note)> Resetting Snowball> SnowRange Note> Snowbear Note (Reverse Snowball)> Snow TARN> Thunderball

Callable:

> Bermudan Callable Note 32

> Callable Zero Coupon Note 34

> Callable Inverse Floater 36

Target Redemption (TARN) 38

> Guaranteed Inverse Floater TARN> Guaranteed Ladder Inverse Floater TARN> Guaranteed Capped Floater TARN> Guaranteed Fixed Range Accrual TARN> Guaranteed SnowRange TARN> Hybrid Coupon TARN

Multi Index 40

> Double Digital Note> Linear Trigger Note> Dual Range Note> Dynamic Cap Note 42

Other ProductsVolatility Note 45

Bond Discount Note 46

Appendix 48

Most Popular Products 49

Structured Note Market 52

Turbo Certificates 54

Interest Rate Models 56

Modelling Processes 58

Yield Curve Considerations 60

Glossary 63

Disclaimer 66

Contacts 67

Methodology 6

Building Blocks 7

Credit Linkage 10

FX Linkage/Quanto 11

Risks 12

Product Map 13

Product DescriptionsFloatersFloating Rate Note 15

CMS/CMT Linked 16

CMS Spread: 18

> Steepener Note (Leveraged CMS Spread Note)> Flattener Note> Digital CMS Spread Note> CMS Spread Range Accrual> Minimum Coupon Spread Note> CMS Spread Inverse Floater

Ratchet: 20

> Ratchet Note> Normal Capped Floater

Range AccrualsRange Accrual: 23

> Normal Range Accrual (lower or upper boundary)> Callable Range Accrual> Corridor Range Accrual> Double Range Accrual> CMS Spread Range Accrual> Minimum Coupon Range Accrual> Floating Range Accrual> Step-up Coupon Range Accrual> Variable CMS Range Accrual

One Look: 26

> One Look Digital Note> Multi Look Note

Table of Contents

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SummaryGiven the highly flexible nature of structured products,attempts to categorise and classify them will always beopen to debate. Nevertheless, certain basic “buildingblocks” apply to all structured products, such as thecoupon/payoff profile, optional features/enhancements,and the redemption structure. Investors should also beaware of some basic concepts, relevant to all products.These include: the importance of the Forward Curve;consideration of possible Yield Curve Movements; theDelta Profile of a note; Vega; and Correlation.

Coupon/Payoff ProfileThe payoff is designed in such a way that it optimallyexpresses the view of the investor. In order to form the “basic product”, the coupon can be tailored in manydifferent ways and linked to an endless variety of indices.Coupon payments can be capped (increasing the participationbut maximising the upside), floored (guaranteeing aminimum coupon), capped and floored (also known as acorridor), or only accrue if certain conditions are met (asin the Range Accrual structure). The investor can choosebetween a (contingent) fixed, floating, inverse floating, orformula-driven coupon. Furthermore, the payoff can bequantoed, thus broadening the scope of indices availablefor the investor to express a view on (see Building Block:FX Linkage).

FeaturesTo enhance returns, investors can add features to their“basic product”. Occasionally, features are so popular that they become products in their own right. Almost allstructured rate products can have the following extrafeatures: Callability; Path Dependency (via the Snowballfamily); Automatic Redemption (as soon as a certaincoupon is reached: Lifetime Cap: TARN); Minimum IRR(Lifetime Floor); dependence on more than one index(Multi Index); Credit Linkage (see Building Block: CreditLinkage); or FX Linkage (see Building Block: FX Linkage:Quanto). Additionally, the fixing of the index can be inarrears (a few business days before the coupon paymentdate) as opposed to normal fixing in advance, in order toexploit the value of the curve.

Redemption StructureStructured notes can also be classified by their redemptionprofile: normal “Bullet” notes have the full notional paidback at maturity; Callable Notes have an unknown maturity(the issuer holds the option of early redemption); TargetRedemption Notes automatically redeem as soon as anaggregate coupon level is reached (TARN); Zero CouponNotes deliver all accrued interest with the notional atmaturity; or the notional can amortise or accrete. Althoughmost structures are capital guaranteed, it is also possible tostructure the note such that (part of) the notional is at risk.

Forward CurvesForward rates are the interest rates between any twofuture periods implied by the current yield curve. Just as the yield curve is a graph of interest rates versusmaturities, forward curves are a graph of forward ratesversus maturities. They are constructed under the principlethat, for example, a one year interest rate will give thesame return as the current six month interest rate,reinvested at the six month interest rate in six month’stime (the 6 month forward rate). So today’s 1 year rateand today’s 6 month rate imply what the 6 month ratewill be in 6 months time. When considering the marketview expressed by a structure, it is important for investorsto realise that it is relative to the forward curve. For example,an expectation of decreasing rates will only be profitableif rates fall by more than implied by the forward curve.

Building Blocks

SummaryAll product profiles have been generated and presentedusing a standardised and rigorous procedure. The layoutof the product profiles is as follows:

Product SummaryThe Product Summary provides a snapshot of the mainfeatures of the basic product, how the coupon is determined,and the potential rate views it may suit. It is worth notingthat the Summary only describes the basic product; withmost structures there is enormous scope for customisation.

Market ViewThe Market View outlines in more detail the view oninterest rates which is expressed through the product.Although the focus is primarily on the basic structure,most products can be customised so as to fit a differentrate view. Importantly, the market view is expressed inrelation to the implied forwards. An investor should onlytake a bearish position if he expects rates to rise morethan implied by the forward rates. If the investor believesthat the rates will rise, but less than implied by the forwards,he should actually take a bullish position. Investors whotake bearish portfolio positions when they expect yieldsto rise (but who ignore the forward rates) may find thattheir positions generate a below-market return despitetheir rate forecast being correct.

Description of ProductThis section explains in more depth the mechanics of thestructure. The product is broken down into its constituentparts, allowing the reader to gain a greater understandingof how it works.

VariationsHere a summary of some of the more popular variationson the basic product is given. Whilst the list can never beexhaustive, it does provide investors with an idea of waysin which the product can be tailored to meet their specificneeds, and indicates the kind of inputs which affect theprofile.

ExampleBasic details of one possible structure are given. Perhapsthe most important aspect of this section is the DeltaProfile, which graphically depicts the interest rate sensitivitythat the specific example has. The delta shows the changein the position’s value resulting from a basis point change inthe underlying interest rate. The delta profile is constructedby shifting one rate at a time by 1 basis point (keeping allother rates constant) and re-valuing the structure.

Sensitivity to Rate MovesThe Delta Profile indicates the yield curve view of thestructure. In general, for maturities displaying positivedelta, the structure benefits from increasing rates, andfor maturities displaying negative delta, the structurebenefits from falling rates. The larger the delta for amaturity, the more impact the interest rate change has on the mark-to-market of the structure. The sensitivity toyield curve movements is summarised diagrammaticallyfor the product specified in the example. Considered area parallel upward and downward shift and a steepeningand a flattening. The “shock” to the level and slope wasstandardised across products. Note also that the steepening/flattening scenarios were driven by rate movements atboth ends of the yield curve (as opposed to a bullish orbearish steepening/flattening – see Basic Concepts) andthat changes in the structure may change the sensitivityto rate moves.

RiskEven though most (but not all) products are capitalguaranteed, there are still inherent risks, which aresummarised in this section. Different risks apply todifferent products. Common risks include (but are notlimited to): coupon risk; reinvestment risk (arising fromcallability); mark-to-market risk; and principal risk (if notcapital guaranteed).

Also ConsiderThis final section suggests alternative structures whichinvestors should consider, based on their market view.Again, investors should be aware of the huge potentialeach product has for customisation.

Methodology

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Yield Curve MovementsInvestors’ primary concern lies with yield curvemovements and changes in shape, because this is what determines their returns. Movements and changesin shape can be split into three components: level, slopeand curvature.

Level: A change in the Level of the yield curve isrepresented by a parallel shift, which shifts yields at every maturity up or down by the same amount.

This type of movement explains the vast majority of yieldcurve movements.

Changes in the Level of the Yield Curve

Slope: A change in the Slope of the yield curve occurswhen long term yields and short term yields becomecloser together (a curve flattening), or when short termyields and long term yields become further apart (a curvesteepening). A curve flattening can be either a bullishflattening (when the flattening is driven by a fall in longterm yields), or a bearish flattening (when driven by a risein short term yields).

Changes in the Slope of the Yield Curve

Similarly, a steepening can be bullish (when driven by afall in short term yields) or bearish (when driven by a risein long term yields).

Curvature: It covers most other movements, which issimply how “curved” the yield curve is. Driven largely by the level of uncertainty over future rate movements,increased curvature is represented by a more “humped”yield curve.

Downward Shift

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Curve Flattening Curve Steepening

Bullish Flattening Bullish Steepening

Bearish Flattening Bearish Steepening

Changes in the Curvature of the Yield Curve

Delta ProfileAn investor’s structured note position is clearly subject to interest rate risk, and the sensitivity to this risk ismeasured by delta. However, the position can be subjectto the interest rate risk across all maturities, not just therates that their coupon is directly referenced to. Hence,the position’s Delta Profile maps out the interest ratesensitivity across all maturities. From this, it is easy tosee the yield curve view that the position expresses.

Delta Profile of a Range Accrual

VegaAnother important indicator of the risk of a structure is its Vega, which measures the structure’s sensitivity tovolatility. Volatility is a key parameter in the pricing ofderivatives and changes in volatility changes the value of a structure.

CorrelationCorrelation is the degree to which one variable fluctuatesin line with another variable. The higher the correlationbetween two variables, the more in line they move.Correlation risk is the risk that due to a change of correlationbetween two indices, the investors structure changes invalue.

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Hence, the overall interest rateview expressed by this positionis of a yield curve flattering.The structure will benefit most iflong term rates fall, and short termrates rise (by a lesser amount)

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Negative delta at longer maturities implies that the structure will benefitfrom falling long term rates

Increased Curvature

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SummaryWhilst most structures in this manual are designed toprovide exposure to interest rates only, ABN AMRO nowoffers investors the possibility to enhance returns byincorporating an element of FX risk. Another possibility is the quanto mechanism, which can broaden the scopeof indices available for the investor to express a view on.With a quanto derivative an exposure can be on an indexin currency A, with the payoff in currency B, or vice versa.Hence, an investor can take advantage of the expectedlevels of many indices in almost any given currency,without being exposed to the associated FX risk.

RationaleFX Linkage (Multi Index)

Demand for additional yield is the main driver behind thegrowing popularity of FX linked interest rate hybrids andother exotic structures. By adding a second constraint,the yield can further be enhanced.

Quanto

A quanto or cross-currency derivative is an instrumentinvolving two currencies. The payoff is determined by a variable measured in one currency, with the payoff in another. Key parameters are the forward value of the underlying, the spot and forward exchange rates, the volatility of the forward FX rate, the volatility of theunderlying forward value, and the correlation betweenthe forward value of the underlying and the forward FXrate. Essentially, a quanto contains an embedded currencyforward with a variable notional amount (“quanto” standsfor quantity adjusting option). The quanto mechanismsuits investors with the view on an index denominated in a certain currency (or investors who want to use thevalue in a particular index) but who want to receive thepayoff in another currency. For structures involving thesale of options, the quanto mechanism allows investors(who “sell” volatility) to benefit from high implied volatility(at inception) of indices in foreign currencies, withoutassuming FX risk or needing to enter into a Cross CurrencySwap. In other words, investors can benefit from steepcurves in other markets, while receiving flows in their

domestic currency, thus avoiding potential FX risk. Quantos are attractive, because they shield the purchaserfrom FX fluctuations.

Foreign ExchangeIn terms of trading volume, the FX market is by far theworld’s largest and most liquid market, with daily tradingvolumes in excess of 1.5 trillion USD. Under normalcircumstances this volume makes it impossible forindividuals or companies to affect FX rates. Even centralbanks and governments find it increasingly difficult toaffect the exchange rates of the most liquid currencies,such as the US Dollar, Japanese Yen, Euro, Swiss Frank,Canadian Dollar or Pound Sterling. The currency exchangemarket is a true 24-hour market, 5 days a week, withdealers in every major time zone. Trading begins Mondaymorning in Sydney (corresponding to 15:00 EST, or 20:00GMT, Sunday) and then moves around the globe throughthe various trading centres, finally closing on Friday at16:30 EST (21:30 GMT) in New York. In the long run, FXlevels are determined by real economic factors such asinterest rates, growth, inflation, trade and investmentflows. However, these economic factors are themselvesinfluenced by the level and volatility of FX. Small changesin the FX rate can have significant effects on (for example)imports and exports, affecting potential future growth.

Examples

A note is denominated in Currency A (say Euros), pays acoupon in Currency A and redeems in Currency A, butthe payoff depends on an index denominated in CurrencyB (for example 6 months USD LIBOR). This is called aQuantoed note.Instead of exposure on a single index (for example 6months EURIBOR), the payoff depends on a secondindex as well (for example the EUR/USD exchange rate).This is called a Multi Index Note.

RisksA bet on multiple indices will increase the probability of abelow-market or zero payout.

Building Blocks – FX Linkage/Quanto

SummaryWhile most structures are designed to provide exposureto interest rates only, ABN AMRO now offers investorsthe possibility to enhance returns by incorporating anelement of credit risk. Credit Linkage can be applied toany structure, which can be made switchable (rather thancallable).

RationaleDemand for additional yield is the main driver for thegrowing popularity of credit linked interest rate hybridsand other exotic structures. Although credit spreads arehistorically low, so is the perceived risk (as expressed in thecredit spread). Companies have de-leveraged significantlyfollowing the excesses of 1999 - 2001, default rates arelow, and (implied) recovery rates high.

SwitchableA Credit Linked structure is usually not callable, butswitchable. For example, a structured note paying a fixed rate which is enhanced by Credit Linkage may be switchable into a “credit only” note with a fixed orfloating coupon payment.

Credit DerivativesWhilst the credit derivatives market has been in existencesince the early 1990’s, it is only since 1999 that the markethas really taken off. Credit derivatives are a class of financialproducts designed to isolate the credit risk of an entity,such as a corporation. Credit risk is a familiar concept - itis the risk that one party owing money to another party,may not pay. The basic building block is the Credit DefaultSwap (CDS), giving an investor regular income in exchangefor the credit risk of a third party. The investor “insures”the counterparty against default. In case of default (calleda Credit Event), the investor has to pay an amount equalto the losses incurred on holding debt of the defaultedcompany. After this, the CDS ceases to exist. In noteform (called a Credit Linked Note; CLN), on an occurrenceof a Credit Event with respect to the Reference Entity,the note will be redeemed at zero and the investor willreceive the Recovery Amount, which is the value of thedefaulted Reference Entity’s bond adjusted for Swap

unwind costs. The Swap unwind costs represent the mark-to-market value of the embedded (and in thismanual described) interest rate swap.

Credit EventsIn the context of credit derivatives, three events aredescribed as defaults: bankruptcy, failure to pay andrestructuring. These events are known as Credit Events.

Bankruptcy: where the Reference Entity becomesinsolvent, placed under administration, or files forChapter 11 protection.

Failure to Pay: where the Reference Entity defaults oninterest or principal payments due on its debt.

Restructuring: where the Reference Entity restructuresthe terms of its debt to the disadvantage of the debtholders.

Multiple NamesInstead of single name exposure, the investor can opt forlinkage to a (linear) basket of Reference Entities, reducingthe exposure on one single name, or increase the leverageby using a First-To-Default (FTD) basket. Leverage canalso be increased or decreased using a synthetic (CDO)structure.

RiskBy embedding exposure on a Reference Entity, thestructure is not principal guaranteed. In the event ofdefault the investors’ note will be redeemed at zero and receive the recovery value (if any) adjusted for swapunwind costs. The investor has mark-to-market exposureto credit spread movements.

Building Blocks – Credit Linkage

Payment upon default

Regular Premium Income

Investor CDS Counter Part

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Yield Enhancement Yield Enhancement

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SummaryAlthough risk is a generally understood concept, it isuseful to define what it means for a buyer of a structuredrate product. Risk in this context entails two essentialcomponents: exposure (to potential loss) and uncertainty(over expected returns). Furthermore, when investing in a note, the investor is exposed both to the movement ofthe underlying as well as to the credit quality of the issuer.Structured rate products often contain “plain vanilla” orhighly exotic embedded options, creating the exposuresought by the investor. As each structured product isunique, the inherent risks may not be obvious. Commonrisks include (but are not limited to) market (interest rate)risk, credit risk, liquidity risk and reinvestment risk. Somerisks (principal risk, mark-to-market risk and coupon risk)are the outcome of the different risk types. These areclosely related but are considered separately to give adeeper insight.

Market RiskMarket risk can impact all asset classes. The value of aninvestment is dependent on the value of the underlyingasset and its variability (volatility). Due to economic changesor other events that impact the market, correspondingchanges in the value and volatility may negatively affectthe value of the investment. Asset allocation anddiversification can be applied to minimise this risk.

Interest Rate RiskInterest rate risk is the risk that the value of the structurechanges due to a change in the absolute level of interestrates, in the difference between two rates, in the shapeof the yield curve or in any other interest rate relationship.

Credit RiskCredit risk is the risk that a loss will be experiencedbecause of a default by the counterparty (issuer). Adowngrade of the issuer will negatively affect the mark-to-market of the investment. The credit quality of anissuer is reflected by its rating as assigned by ratingagencies and by its credit spread in the market. Over thelife of the transaction, the investor is exposed to achange in the credit quality of the issuer. In the event of

a default, the investor might either receive a fraction of the notional (the “recovery rate”) or lose the full notionalinvested (worst case scenario).

Reinvestment RiskIf the note is callable the issuer has the right to redeemthe structure early. Where this happens the investor may have to reinvest into another structure with lessadvantageous conditions in the market.

Liquidity RiskLiquidity risk is the risk that arises from the difficulty ofselling an asset or note. Some assets are highly liquidand have low liquidity risk (like a stock of a public tradedcompany), while other assets are highly illiquid (such asproperty). Under certain market conditions a structurednote might be difficult to offset either because the unwindcosts are relative high or because it is difficult to find acounterparty.

Coupon RiskIn a structured rate product, the coupon is usuallyconditional upon specific levels, barriers or triggers. Ahigh coupon will be paid if the embedded view proves to be correct, a below market or even zero coupon willaccrue if the view proves to be (partly) incorrect. Back-tests or forward projections are not a guarantee ofrealizing the projected coupons.

Principal RiskPrincipal risk, the risk of losing (part of) the notional, canbe divided into: 1) risk of the issuer defaulting (this aspectis covered in credit risk) and 2) the possibility to structurethe note such that (part of) the notional is at risk.

Mark-to-Market RiskThe mark-to-market (MtM) of an investment is its value ata specific moment. Over time the MtM of an investmentmay be positive or negative due to all the above elements,and other less obvious factors such as volatility andcorrelation, but it is important to Note that at maturityredemption is at the pre-agreed level (mostly Par).

Risks

Higher Rates

Stable Rates

Lower Rates

Steepening

Flattening

Product Map

Client’s Attitude to Risk

Client’s View Aggressive Medium Conservative

>Multi Index Note > Ratchet Note> Step-Up Lower Boundary > Floating Lower Boundary

Range Accrual > Floating Lower Boundary Range Accrual> One Look Note Range Accrual > CMS Linked Note> Snowbear Note > Floating Range Accrual > Capped Floater

> Lower Boundary Range > Multi Look Note > Minimum Coupon RangeAccrual TARN Accrual

> Geared CMS Note > Floating Rate Note> Turbo Short Bond Future > Capped CMS Note

> Corridor Range Accrual > (Callable) Range Accrual> SnowRange Note > Corridor Range Accrual > (Callable) Zero Coupon Note

> Target Redemption Note > Callable Range Accrual > Callable Note> Bond Discount Note > Bond Discount Note > Ratchet Note

> Snowball > Callable Zero Coupon Note > Normal Bond> One Look Note > Resetting Snowball > Minimum Coupon Range

> Callable Inverse Floater > Multi Look Note Accrual> Multi Index Note

> Upper Boundary Range Accrual> One Look Note > Callable Zero Coupon Note > Normal Bond

> Leveraged Inverse Floater > Upper Boundary Range Accrual > Upper Boundary Range Accrual> SnowRange Note > Callable Inverse Floater > Bermudan Callable Note

> Thunderball & Snowball > Bond Discount Note > Minimum Coupon Range> Target Redemption Note > Resetting Snowball Accrual

> Multi Index Note > Multi Look Note > (Callable) Zero Coupon> Snow TARN

> Turbo Long Bond Future

> Leveraged Steepener Note > CMS Spread Range Accrual > CMS Spread Range Accrual> Digital CMS Spread Note > Digital CMS Spread Note > CMS Linked Note> One Look Note (on CMS) > Dynamic Cap Note > Minimum Coupon Spread Note

> Multi Index Note > Dynamic Cap Note

> Leveraged Flattening Note> Target Redemption Note > CMS Spread Range Accrual > CMS Spread Range Accrual

> SnowRange Note > Digital CMS Spread Note > Minimum Coupon Spread Note> Digital CMS Spread Note

> Multi Index Note

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SummaryA Floating Rate Note (FRN) suits an investor with theview that interest rates will go up, or who wants to beprotected against rising interest rates. An FRN is a notewhose interest rate is periodically adjusted according tothe interest rate of a specified short term index. Thesenotes are also known as Floaters.

Market ViewAn FRN suits an investor with the view of increasing rates(or higher future rates than implied by the forwards) or aninvestor who does not want delta exposure on the yieldcurve (i.e. likes the note to trade around Par regardless ofinterest rate movements). The investor is therefore hedgedagainst the consequences of rate moves.

Description of ProductAn FRN is similar to a vanilla interest rate swap, anagreement between two counterparties to swap a floatinginterest rate for a fixed interest rate (or vice versa), basedon a pre-agreed amount, term and conventions. The cashflows are exchanged at the end of each interest period. Inan FRN, the investor gives the notional to the issuer andin return receives floating interest payments. The fixing ofthe floating interest payment is normally in advance (i.e.2 business days before the start of the coupon period) andthe payment in arrears (at the end of the coupon period,on the coupon payment date). So, in a normal FRN thefirst coupon is already fixed.

VariationsThe coupon can be capped to increase the participationor add a spread above the floating rate (Capped Floater)The coupon can be floored to guarantee a minimumcouponA Corridor can be constructed which minimises andmaximises the couponThe fixing can be in arrears, with the floating rate fixing afew days before the coupon payment date, rather than atthe start of the coupon periodIt is possible to construct an Inverse Floater variant if ratesare expected to decrease

Example: Floating Rate Note

Currency EURMaturity 5 yearsCoupon 6M EURIBOR + 3bps, s.a. 30/360ABN Receives Notional

Delta Profile of 5Y FRN

In the graph the delta profile of the 5 year FRN showsthe interest rate sensitivity of the structure. The 5 yearnegative delta seems large but is very small on anabsolute basis. As expected for a floating instrument, the sensitivity to interest rate moves is minimal.

Sensitivity to Rate MovesAn FRN has no significant sensitivity to curve moves.

RisksA decrease in rates or a smaller increase than implied by the forwards will result in an opportunityloss versus a fixed coupon security.

Also ConsiderCMS linked NoteCapped FloaterRatchet Note

Attitude to Risk: Conservative

Floating Rate Note (FRN)

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Sensitivity to Rate MovesOverall, the structure benefits from a steepening of theyield curve. Parallel shifts should not have too much of an impact as the underlying swap is floating-for-floating.However, since the participation level is different (82.5%of the 10 year versus 100% of the 6-months), the deltashave a slightly different weighting and could result insome (although limited) parallel shift exposure. The CMSLinked Note is attractive when the forward swap curve isflat as it will increase the participation level (or gearing) inthe longer dated rate.

RisksA Flattening of the curve will have a negative impact onthe mark-to-market of the structure.

When transacted in note form, the note may trade belowpar during the life of the transaction.

Also ConsiderSteepener NoteCMS Spread Range Accrual with CMS coupon


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Curve SteepeningA steepeningof the yieldcurve will bepositive forthe structure.A parallelshift will havelimited impact.

Downward Shift

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Curve FlatteningA flatteningof the yieldcurve will benegative forthe structure.A parallelshift will havelimited impact.

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SummaryA CMS Linked Note suits an investor with the view thatthe yield curve will steepen. The coupon payment in aCMS Linked Note is referenced to a constant maturityswap rate, which is periodically reset. Also possible is aConstant Maturity Treasury (CMT) which is referenced toa particular maturity US Treasury.

Market ViewCMS Linked Notes suit investors with the view that theyield curve will steepen. Although the coupon paymentwill benefit from an increase in the indexed (long term)rate, if the curve shape doesn’t change, the mark-to-market effect of the parallel upward (downward) shift is small as the funding costs (i.e. the short term rate)increases (decreases) as well. A CMS Linked Note isespecially attractive in a flat yield curve environment.

Description of ProductA Constant Maturity Swap is a floating-for-floating interestrate swap, exchanging a LIBOR Rate for a particular swaprate. By referencing to longer term constant maturityswap rates (typically between 2 and 30 years), the CMSLinked Note enables investors to gain a floating exposureto a longer term rate. The investor profits from an increasein volatility due to the convexity adjustment (the investor issaid to be “long Vega”). Convexity measures the curvaturein the relationship between bond prices and their yields.Bonds with high convexity perform better if rates change;if rates fall their price rises by more, if rates rise theirprice falls by less. The benefits of convexity cause moreconvex bonds to have higher prices and consequentlylower yields.

VariationsThe CMS coupon can be capped, increasing theparticipation level in the CMS but limiting the upsideThe CMS coupon can be floored, guaranteeing aminimum payment, but decreasing the participationA corridor can be constructed to minimise and maximisethe CMS couponIt is possible to construct an inverse floater variant, wherebythe investor profits from a decline in a specified CMS rate

Example: CMS Linked Note

Currency EURMaturity 10 yearsCoupon 82.50% of the 10Y CMSABN receives 6M EURIBOR or Notional

The delta profile of the CMS Linked Note is shown thegraph. The 10Y delta is negative as the note is a 10Ystructure and the 10Y delta represents the notional as inany floating rate instrument. It is the longer dated yieldswhich reflect the implied 10Y constant maturity rate.Hence, the structure benefits from rising rates for currentmaturities of eleven years or more. Conversely, thestructure benefits from falling rates for current maturitiesof ten years or less.

CMS/CMT Linked Note

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Example: CMS Spread Range Accrual

Currency EURMaturity 20 yearsCoupon (5.10% x N/M) annual, 30/360N Number of days (10Y CMS - 2Y CMS) > 0M Total Number of DaysABN Receives 6M EURIBOR or Notional

Delta Profile of a CMS Spread Range Accrual

In the graph the delta profile of the CMS Spread RangeAccrual is shown. As the structure has a fixed (rangeaccrual) coupon, the negative delta in year 20 is expected(i.e. the investor prefers rates to go down), although partof the delta is the notional effect as it is a 20 year note.The interesting part is the positive delta in 25 year and 30 year. As the investor is basically long the 10Y CMSand short the 2Y CMS, the positive delta in year 30 isexplained as the 10Y CMS rate in year 20, which theinvestor obviously prefers to go up as it increases theprobability of a positive curve. The sensitivity to curveflattening and steepening is more complex.

Although the structure obviously likes the curve to staypositive sloping (and a steepening of the curve increasesthe probability of receiving the coupon), a steepening ofthe curve also increases the probability that the fixed(range accrual) coupon will be below the market rate andhence have a negative impact on the mark-to-market ofthe structure.

Sensitivity to Rate Moves

RisksAn adverse movement of the curve can result in a belowmarket or zero coupon structure (worst case scenario:annual coupons of 0.00% with a value of the structureclose to a Zero Coupon Note).


Also ConsiderTarget Redemption Notes (if expecting a flatter curve)CMS Note (if expecting a steeper curve)

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20

0

-20

-40

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Curve SteepeningA parallel shiftdownwards willnormally bepositive for thestructure as thecoupon is fixed.The effect ofa slope movedepends on therelative level ofthe curve.

Downward Shift

Maturity

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Maturity

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Curve FlatteningA parallel shiftupwards willnormally benegative for thestructure as thecoupon is fixed.The effect ofa slope movedepends on therelative level ofthe curve.

Upward Shift

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Attitude to Risk: All

SummaryA CMS Spread Note suits an investor with a view on the curvature and slope of the yield curve. The payoffdepends on the difference between two indices and can suit a steepening, flattening and stable curve view.

Market ViewCMS Spread Notes suit investors with the view that achosen spread will remain relatively unchanged, becomebigger or become smaller than that implied by the forwardsfor the index. CMS Spread Notes can therefore be used indifferent interest rate environments. If an investor expectsa steepening of the curve, a note paying a multiple of thedifference between 2 indices may be appropriate (forexample: 8 x (10Y – 2Y)). If the curve becomes steeper,the investor profits significantly. The investor only achievesan above market return if the curve steepens more thanimplied by the forwards. The flatter the curve, the moreleverage is possible. If the investor’s view is of a flatteningcurve, a Flattener (similar to an Inverse Floater) will beattractive. Here the investor receives a high fixed couponminus the (leveraged) difference between 2 indices, andreceives a higher coupon if the curve flattens. Anotheralternative is a CMS Spread Range Accrual, which accruesa high coupon for every day the difference between twoindices stays above a certain strike. This is currently apopular trade in the market, with many investors bettingagainst an inversion of the EUR yield curve. Currentforward rates imply that 2Y rates will exceed 10Y rates in 2018, and if the investor’s view is digital by nature (i.e.the investor thinks the curve will not invert) the CMSSpread Range Accrual is an attractive option.

Description of ProductIn a Steepener or Flattener structure the investor is ineffect buying a series of caps to ensure the coupon hereceives is floored at zero. In the Steepener the investorbuys the cap on the short term rate. In a Flattener theinvestor buys the cap on the long term rate. In a CMSSpread Range Accrual the client sells a series of dailyDigital CMS Spread Floors. ABN AMRO would receive aday’s worth of coupon for every day the curve is inverse,and the client receives coupons for days when the curveis not inverted. Since two indices are involved, correlationis important. In general, when buying a CMS Spread RangeAccrual (assuming the investor sells out-of-the-moneyoptions), investors prefer low correlation at inception,because they will get a higher yield pick-up (since lowercorrelation makes it more likely for the structure to breachthe range). After trading, the investor prefers high correlation(if the option he sold is still out-of-the-money) becausethe likelihood of the spread between the two indicesbreaching the range would be lower, giving a positiveeffect on the mark-to-market of the structure (the investoris said to be “long” correlation). Once the option soldbecomes in-the-money the investor prefers correlation to decrease, making it more likely that the curvature willmove back in his favour. Higher volatility of the spread atinception will increase the coupon.

VariationsThe structure can leverage on a steepening of the curve(Steepener Note) by paying a coupon of X times (10Y – 2Y)The structure can leverage on a flattening of the curve(Flattener Note) by paying a coupon of X – (Y times (10Y – 2Y))The CMS Spread Range Accrual Note (see example)accrues a day’s worth of coupon for every day the CMSspread fixes within a predefined rangeA Digital CMS Spread Note pays a certain coupon if theCMS Spread meets a predefined condition; otherwisethe investor (typically) receives a 0% couponCMS Spread Notes can be done in inverse floater format

CMS Spread Note

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20 21

A hypothetical interest rate scenario

Coupon 6M USD LIBOR + 40bpsRatchet cap 25bps per quarter

6M USD LIBOR fixing Coupon 1st fixing 4.00% 4.40%2nd fixing 4.25% 4.65%3rd fixing 4.60% 4.90%4th fixing 4.80% 5.15%5th fixing 5.00% 5.40%6th fixing 5.50% 5.65%7th fixing 5.90% 5.90%8th fixing 6.30% 6.15%

In the above example it is obvious that a modest increasein rates will result in an above market coupon. In a scenarioof rapidly increasing rates the note will under perform anormal Floating Rate Note.

Hypothetical Interest Rate Scenario and Ratchet Coupon


RisksA spike in interest rates could result in a below-marketcoupon.


Also ConsiderCapped CMSCapped Floater

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1st 2nd 3rd 4th 5th 6th 7th 8thfixing fixing fixing fixing fixing fixing fixing fixing

Coupon

6.5%

5.5%

4.5%

3.5%

6M $L Fixing

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Curve Steepening

A parallel shiftdownwards ora flattening ofthe yield curvewill normally bepositive for thestructure.

Downward Shift

Maturity

Yie

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Maturity

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Curve Flattening

A parallel shiftupwards ora steepening ofthe yield curvewill normally benegative for thestructure.

Upward Shift

Maturity

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Ratchet Note

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SummaryA Ratchet Note suits an investor with the view that rateswill go up but by less than implied by the forwards. ARatchet Note pays a floating rate coupon that is onlyallowed to increase by a certain amount per period.

Market ViewThe Ratchet Note suits an environment with steep yieldcurves and high volatility (at inception) which allows asubstantial yield pick up to be achieved. The structuresuits an investor with the view that rates will rise, butthat large and quick increases in rates (as perhaps impliedby the forwards) will not materialise. The main risk for theinvestor is therefore a scenario in which rates spike upvery quickly, in which case the coupon will lag a normalFloating Rate Note and need several periods of stablerates in order to catch up again.

Description of ProductA Ratchet Note is an instrument in which each successivecoupon is capped in some way by the previous couponpayment. The Ratchet Note is basically a note in whichthe investor sells a string of caplets for which only thefirst caplet strike is set. For the successive caplets thestrike is reset on predetermined roll dates. The level atwhich the strike is set is dependent on earlier strikes and fixings. The main feature is the fact that the jumps in the strike level are restricted to a certain maximum (i.e.the strike is not allowed to jump by more than 25bps).

VariationsDifferent underlying indices are possible, although someindices (for example, CMS indices) tend to have lesssteep forwardsInstead of a ratchet cap (i.e. a maximum increase of25bps per fixing) a normal coupon cap can be applied (i.e. the coupon cap for year 1 is 4.00%, for year 2:4.25% etc)

Example: Ratchet Cap

Currency USDMaturity 5 yearsCoupon 3M USD LIBOR + 40bps, qu 30/360Ratchet cap 25bps per quarterABN receives 3M USD LIBOR or Notional

Delta Profile of a Ratchet Cap

In the graph the delta profile of the Ratchet Note isshown. As expected, the investor prefers the short termrate to go up slightly. The exposure to 5 year rates ismainly the fact that it is a 5 year structure and partly thefact that as the investor has sold caps, an increase in the5 year rate (which is the present value of the 3 monthforwards) indicates an increase in short term rates, whichis capped. The options sold therefore become more in-the-money, reducing the value of the swap. As a result,the investor prefers 5 year rates to decrease (slightly).

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Range Accruals (RA)

SummaryA Range Accrual suits an investor with the view that anindex will stay within (or outside) a given range. For eachday the investor is correct he accrues one day’s worth ofcoupon, otherwise a below-market coupon accrues(usually 0%).

Market ViewRange Accruals work in different rate scenarios: if futurerates are expected to be higher than implied by the forwards,a lower boundary only range accrual is a suitable and yieldenhancing structure. If future rates are expected to belower, an Upper Boundary Range Accrual works. CorridorRange Accruals suit a stable rate environment, a ratemove as implied by the forwards or a specific path asexpected by the investor.

Description of ProductA simple Range Accrual is basically a strip of digital options,one for each day of the accrual period. The investor sellsthese options in return for an above-market coupon. Sincethe client sells the options, volatility is an important element.Most of these options will have out-of-the-money strikesand the higher the volatility at inception, the more valuethe options will have, and the higher the coupon will be. Ifafter the trade the implied volatility increases (decreases)the mark-to-market of the swap will decrease (increase).Many Range Accruals are made Bermudan Callable toenhance the coupon. If the structure is Bermudan Callable,the investor has sold ABN AMRO the option to call thestructure (redeem early) at a pre-determined level (usually100%) on pre-determined dates through the life of thenote. The option sold to ABN AMRO is a Receiver (Range)Bermudan Swaption. The buyer of the Receiver BermudanSwaption has the right to exchange a stream of floatinginterest rate payments for a stream of fixed interest ratepayments (in this case a range accrual payment), beginningat a future date for a pre-agreed amount, based upon pre-agreed conventions (i.e. a receiver swaption is the right

to receive the fixed rate), and on pre-agreed dates. By making the structure callable, the investor is exposed toswaption volatility. The investor prefers high volatility atinception as this will enhance his coupon. For each periodthe coupon is determined by counting the number ofdays the reference index stays within the range versusthe number of days in that period. Assume for reasons ofsimplicity the note has a maturity of 1-year (consisting of360 days):

If 187 days are within the range, the coupon is: 187/360 xcoupon of (for example) 7.25% = 3.76%If all days are within the range, the full coupon will bepaid: 360/360 x 7.25% = 7.25%

VariationsThe index can be LIBOR, CMS, FX, or the spreadbetween 2 indices (CMS Spread Range Accrual). Thestructure can also be dependent on two indices (DoubleRange Accrual)The coupon can be fixed, floating (Floating RangeAccrual) or step-up (Step-Up Coupon Range Accrual). AStep Up Coupon Range Accrual works well in a steepforward curve environmentIt is possible to have a lower boundary only, an upperboundary only, a corridor (Corridor Range Accrual), step-up or step-down barriersThe frequency with which the index is observed can bedaily, weekly, monthly, etc. Daily is the most commonRange accruals can be made (Bermudan) callable (andmost are in order to achieve yield enhancement): CallableRange AccrualsThe structure can have a minimum coupon (MinimumCoupon Range Accrual)The structure can have a different reference index everyyear (i.e. the 10Y in 1Y, the 9Y in 2Y etc): Variable CMSRange Accrual

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Example 1: Callable Corridor RA

Currency USDMaturity 5 yearsCoupon 7.25% x N/M, qu 30/360 (5Y = 4.70%)ABN receives 3M USD LIBOR – 11bps or NotionalRef index 3M USD LIBORRange Y1 - Y2: 3.00% - 5.50%

Y3 - Y5: 3.00% - 6.00%Callable Quarterly

Delta Profile of 5Y Callable Corridor RA

In the graph above the delta profile of the example 5 yearCorridor Callable Range Accrual is shown. The delta profiledepicts the interest rate sensitivity of the structure. It isclear that the investor wants longer dated rates to go down:since the longer dated rates are basically the present valueof a string of forwards, it is far more important for thevalue of the structure that the longer dated rates movesin the investors favour than the 3 month spot rate, whichwill “only” affect a single coupon payment. The delta profileshows that the client profits from a curve flattening.

3M USD LIBOR Forwards against Specified Boundaries

In this graph the 3 month USD LIBOR forward interestrate is shown versus the chosen boundaries in abovementioned example. Note that according to the forwardsthe coupon is paid in full.


Example 2: Floating CMS spread RA

Currency USDMaturity 15 yearsCoupon 10Y CMS + 35bps IF (10Y - 2Y CMS) > 0ABN receives 3M USD LIBOR or Notional

Delta Profile of Floating CMS Spread RA

In the graph above the delta profile of the exampleFloating CMS Spread RA is shown. As expected, theinvestor profits from a curve steepening and increase inthe longer dated rates. The exposure to 15 year rates ispartly the representation of paying the short term floatingrate in the swap, which the investor prefers to decrease.Part of this is the notional effect: it is a 15-year trade.

Floating CMS Spread RA Payoff Profile


RisksAn unanticipated move of the chosen reference index canresult in a low coupon or zero coupon structure (worstcase scenario: all fixings outside the range, resulting in a0.00% coupon and a value of the structure close to thevalue of a Zero Coupon Note).

The structure is sensitive to absolute changes in ratesand implied volatility.

When the structure is callable, the investor is exposed toreinvestment risk.


Also ConsiderSnowRange NoteMulti Index Note Bermudan Callable Note

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2005 2009 2013 2017 2021 2025

Coupon

5

4

3

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1

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10yr Swap 10yr-2yr

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Curve SteepeningA steepeningof the yieldcurve will bepositive forthe structure.A parallelshift will havelimited impact.

Downward Shift

Maturity

Yie

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Curve FlatteningA flatteningof the yieldcurve will benegative forthe structure.A parallelshift will havelimited impact.

Upward Shift

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Oct 05 Oct 06 Oct 07 Oct 08 Oct 09 Oct 10

Upper

6.5

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Curve Steepening


Downward Shift

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Upward Shift

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26 27

Attitude to Risk: Aggressive

SummaryA One Look Note suits an investor with a short termview on an index. If correct, the investor receives asignificant above-market coupon. The payout of a OneLook Note is digital: if the view proves to be correct afixed cash amount will be paid; if the single fixing isoutside the range no payment will take place.

Market ViewA One Look Note suits any interest rate environment. If aninvestor expects rates to be stable, the coupon paymentcan be contingent upon a fixing within a predefined corridor.If the investor expects interest rates to go up, they canreceive an above-market coupon dependant upon a fixingabove a certain strike. If rates are expected to decline, afixing below a certain strike level would result in the fixedpayoff. One Look Notes are well suited for short term views.

Description of ProductIn a One Look Note the investor sells a European digitaloption (where the payout is either a fixed cash amount or nothing at a predefined date) to the issuer. Whilst anormal swap fixes at the beginning of (or typically a fewdays before) the observation period, here the fixing is inarrears (postponed until the end of, or a few days beforethe end of the observation period). In either case,payments take place at the end (see graph below).

Fixing-in-arrears

In a One Look Note only the fixing counts; the path followed by the index is irrelevant. Also, the degree thatthe option is in or out-of-the-money doesn’t matter. Thereis no difference of being “just right” or “really right”. Thestructure can be designed to be sensitive to the pathtaken. With knock-in and knock-out options a couponpayoff can be structured which will have a zero payout if a certain barrier is breached or pays out at the moment acertain barrier is hit. Most of the time investors sell near-the-money digital options. At time of trading, the investorprefers the volatility to be high so he receives moreupfront premium. After inception the volatility preferenceall depends on the movement of the index relative to theposition of the investor. If the reference index is at theright side of the fixing for the investor, the investor prefersvolatility to be low. If on the other hand the index is onthe “wrong” side, the investor prefers volatility to moveup so the possibility that the fixing will be positive forhim increases somewhat. Notice that as the investor hassold the option, an out-of-the-money option is profitablefor him.

VariationsInstead of a One Look, a Multi Look Note can bestructured (i.e. every fixing is a digital payout regardlessof the path and previous fixings)A normal One Look Note is 3-months up to 1-year, butwith multiple fixings a longer maturity is possibleInstead of a short term interest rate index, swap rates,FX, commodities or double indices (i.e. exposure on twoindices) are possible

Example: One Look (Digital) Note

Currency EURMaturity 1 yearCoupon 5.00% if 10Y EUR CMS fixes at or above

3.60% at maturity (10Y Euro spot = 3.23%)0.00% if 10Y EUR CMS fixes below 3.60%

ABN receives 3M EURIBOR - 6bps or Notional

Delta Profile of 1Y Digital Note on 10Y CMS

The graph above shows the exposure of the note to the11 year interest rate and the 1 year rate. As the note is aone year structure, the negative delta in year one can beexplained as the notional effect. The main exposure is tothe 10 year rate at the end of year one (the 11 year rate),which the investor likes to go up. Overall the investorprefers the curve to steepen.


RisksAn adverse movement of the reference index can resultin a zero pay out (worst case scenario: a 0.00% couponand if multiple fixings, a value of the structure close tothe value of a Zero Coupon Note).

As the fixing is digital, even if the investor is correct for99% of the time, the single fixing can still be outside therange.

The note may trade below par during the life of thetransaction.

Also ConsiderBond Discount Note

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Curve Steepening

A parallel shiftdownwards ora flattening ofthe yield curvewill normally benegative for thestructure.

Downward Shift

Maturity

Yie

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Maturity

Yie

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Curve Flattening

A parallel shiftupwards ora steepening ofthe yield curvewill normally bepositive for thestructure.

Upward Shift

Maturity

Yie

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Normal Fixing Start Observation Period

In-arrears Fixing

Payment Date

One Look Digital Note

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Snowball (Ladder) Note

SummaryA Snowball Note suits an investor with the view thatinterest rates will remain within a pre-defined band or(with the most popular structures) decrease (or increaseless than implied by the forward) over time. The Snowballshould be seen as a feature which can be embedded inmany structures, allowing the coupon to accumulate byreferring back to the previous coupon. In other words,future coupons rely on past coupons.

Market ViewThe most popular Snowball is the inverse floating variant,designed for investors who believe that the yield curve isrelatively steep and that forward rates overestimate theincrease in spot rates in the future or expect rates to staystable or decrease. They generate a significant yield pick-up by betting against the forward curve with leverage. Asthe Snowball feature refers back to the previous coupon, thecoupon is path dependent by nature, adding value (leverage)for an investor with a specific view. The structure worksbest in a steep yield curve environment.

Description of ProductThe Snowball is also known as a “Ladder”. The mainfeatures of a Snowball are the inverse floater part (in theform of: Fixed Rate – (X x Floating Rate)), the snowballitself (Previous Coupon + Inverse Floater) and if callable,the Bermudan Swaption, which will increase the FixedRate or Gearing. In a Snowball, the client sells a call optionto ABN AMRO at par and buys a series of caps with amoving strike as the coupons are floored at zero. The capis equal to the previous coupon + fixed amount. Supposethe previous coupon is 5% and the fixed amount is 2%(making the coupon formula: Previous coupon + 2% - 12MEURIBOR in arrears), the cap the investor bought is at 7%(because otherwise the coupon could become negative).The coupon payoff from a Snowball is sensitive to changesin the shape of the yield curve and volatility curve.

VariationsThe index can be LIBOR, CMS, FX or the spreadbetween 2 indicesInstead of speculating on a decrease in rates via theInverse Floater variant, it is possible to construct theSnowball in such a way that the payout benefits from anincrease in rates (called a Reverse Snowball or Snowbear)A Lifetime Cap can be added to construct a TargetRedemption Note variant (Snow TARN)A very popular structure is the Callable SnowRange. Thisproduct is a combination of a Range Accrual, a Snowballand a Bermudan Swaption (see example 2)To reduce the path dependency risk, it is possible tostructure a Resetting Snowball. In this structure thecoupon resets automatically at predetermined datesIt is possible to leverage the previous coupon so thecoupon formula is [(Gearing x Previous Coupon) – 3M USD LIBOR in-arrears]. This structure is known as a Thunderball

Example 1: Snowball

Currency EURMaturity 7 yearsCoupon Y1: 5.75%, s.a. 30/360

Y2 - Y7: (Previous coupon + 2.50% - 6MEURIBOR (in arrears)), floored at 0%

Callability Semi annuallyABN receives 6M EURIBOR or Notional

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Delta Profile of a Snowball Note

In the previous graph the delta profile of the exampleSnowball structure is shown. As expected, the investorprefers rates to decrease.

Snowball Payoff Profile


As expected, a flattening curve will generate a positivemark-to-market for the investor. This effect is enhancedas a result of the effects of gearing and the pathdependent nature of the coupons.

Callable SnowRange

Currency USDMaturity 5 yearsCoupon 6M: 7.00% x N/M

Thereafter: (Prev coupon + 0.50%) x N/MN number of days 6M USD LIBOR is within

range M total number of daysRange 3.50% - 6.00%Callability Semi annuallyABN receives 3M USD LIBOR or Notional

In a SnowRange, the coupon is determined by countingthe number of days within the range versus the numberof days in that period, multiplied by the previous coupon.The coupon payment is therefore highly path dependent;once a coupon is reduced due to a period of fixings outsidethe range, future payouts will always be equal at best orlower than the previous coupon, even if the investor iscontinuously correct in the subsequent periods. Theadvantage of a SnowRange over a normal Callable RangeAccrual is the additional pick up in yield if the view provesto be correct.

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SnowRange Payoff Profile

SnowRange Coupon Calculation

Assume for reasons of simplicity a period of 3-years(consisting of 3 x 360 days) and an initial coupon of7.00%:

If in year 1 all days are within the range, the coupon atthe end of year one will be: 7.00% x 360/360 = 7.00%.

Suppose in year 2 only 180 days are within the range: the new (now maximum) coupon for the note is 7.00% x 180/360 = 3.50%. If in year 3 all days are back in therange again, the new coupon would be 3.50% x 360/360= 3.50%.

RisksThe structure is sensitive to absolute changes in ratesand implied volatility.

The path dependent nature of Snowball structures canresult in a below-market coupon or even zero coupondespite the view of the investor being correct for most ofthe time (i.e. the timing of being right is very important:the most risk is early in the life of the note). The worstcase scenario is 0.00% coupons during the life of thenote and a value of the structure close to the value of a Zero Coupon Note.


Also ConsiderTarget Redemption NoteCallable Range Accrual

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SummaryA Bermudan Callable Note suits an investor with the viewthat the long term rates will not rise as quickly as theforwards suggest or expects rates to be stable. Investorsachieve a pick-up over the equivalent reference rate byselling ABN AMRO the option to call the structure (redeemearly) at a pre-determined level (usually 100%) on pre-determined dates through the life of the note.

Market ViewA Bermudan Callable Structure is most attractive if theinvestor believes that the market will be relatively stableor that rates will rise less than implied by the forwards. Ifthe investor expects rates to go down, he will buy a fixedrate security. If he expects rates to go up, he will prefer afloating rate instrument. The embedded Bermudan optionallows the investor to achieve a coupon pick-up in returnfor the risk of early redemption. The investor sacrifices aknown duration of a normal bond for a higher yield anduncertain duration of a Bermudan Callable Note.

Description of ProductIn a Callable Note, the investor sells a call option with astrike at 100% to the issuer, meaning that he sold the right(but not the obligation) to redeem the notes at 100% onany given call date. For this the investor is compensatedby an option premium, which will be paid in the form of ahigher coupon. The option sold is a Bermudan Swaption,giving the buyer the right to exchange a stream of floatinginterest rate payments for a stream of fixed interest ratepayments, beginning at a future date for a pre-agreed amountand based upon pre-agreed conventions. This embeddedoption in the note shortens the duration of the note and leadsto negative convexity: when yields fall, the duration falls tooas it becomes more likely that the call will be exercised. Theyield pick-up of a Callable Note over the fixed rate dependson several factors. Higher maturity, volatility and steepnessof the forward curve generally increase the yield pick-up.Investors are essentially selling swaption volatility andprefer high volatility at inception of the trade as this willenhance their coupon. The reason behind the BermudanCallable Note’s popularity is the fact that most investorsprefer uncertainty in maturity over uncertainty in yield.

VariationsThe number of calls and the first call is flexible (i.e.5YNonCall6M, 5YNC2Y)The coupon structure can step up (for example in anenvironment where the curve is very steep: as the stepup is in line with the forward rates it increases the optionvalue). This is a Step-Up Callable Note

Example: Bermudan Callable Note

Currency EURMaturity 10 yearsCoupon 3.55%, s.a 30/360 (10Y ref rate 3.23%)ABN receives 6M EURIBOR – 11bps or NotionalCallable NC12M, thereafter semi-annual

Delta Profile of a 10Y Callable Note

In the graph above the delta profile is shown. Asexpected, the main sensitivity is to 10 year interest rates. A decrease in the 10 year rate will increase themark-to-market value of the structure.


If interest rates move up, the probability that the note will be called decreases (assuming constant volatility). If interest rates move down, the likelihood of the notebeing called increases. As the investor has sold anoption, an increase in implied volatility will decrease the mark-to-market value of the structure; a decrease inimplied volatility will increase the value of the structure(and also increase the probability of being called).

RisksAn increase in rates can result in a mark-to-market loss(the note will trade below par), as with any fixed rateinstrument (an opportunity loss).

The structure is sensitive to changes in volatility.

If interest rates fall and the structure is called, theinvestor is exposed to reinvestment risk.

Also ConsiderCallable Zero Coupon NoteCallable Range Accrual with a “wide” range

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Attitude to Risk: Medium Conservative

SummaryA Callable Zero Coupon Note suits an investor whoexpects rates to be stable, or has the view that the longterm rate will not rise as quickly as implied by the forwards.A yield pick-up over the equivalent reference rate is achievedby selling ABN AMRO the option to call the structure(redeem early) at a pre-determined level on pre-determineddates throughout the life of the note. As the name suggestscoupons are not paid during the life of the note, but areautomatically reinvested at a fixed annual rate of return,and paid at maturity. A popular variant is the Zero AccretingSwap, in which an annual coupon is paid, but over anaccreting notional. It replicates the normal zero couponstructure, but lowers the credit risk for the investor onthe counterparty.

Market ViewA Callable Zero structure is most attractive for an investorwho does not need a regular cash flow, and believes thatthe market will be relatively stable or that the forwardsimply that rates will not rise by too much. If the investorbelieves rates will decrease a Normal (Non Callable) ZeroCoupon is a well suited product as it has a duration equalto its maturity (i.e. high interest rate sensitivity) and theinvestor is not exposed to reinvestment risk. The advantageis that a Zero Coupon Note will generally have a higheryield than a coupon bearing note in an upward slopingyield curve environment. Another reason for buying aZero Coupon Note could be the desire to defer tax oninterest until a later date. In a Callable Zero Coupon theinvestor sacrifices a known duration of a straight zerocoupon bond for a higher yield and uncertain duration.

Description of ProductIn a Callable Zero Coupon Note, the investor sells a calloption to the issuer, meaning that the investor has soldthe right (but not the obligation) to redeem the note at apredetermined level and call date. For this the investor iscompensated by an option premium, which will be paid in the form of an enhanced fixed internal rate of return(IRR). The option sold is actually a Receiver BermudanSwaption. The IRR will be higher when the Swaptionvolatility at inception is higher. The embedded option in the note shortens its duration and leads to negativeconvexity: when yields fall, the duration falls too as itbecomes more likely that the call will be exercised. TheIRR of a Callable Zero Coupon Note therefore dependson the shape of the curve and volatility.

VariationsZero Coupon Notes can be callable or non-callable (withno reinvestment risk). The yield of a Callable Zero Couponwill look more attractive relative to a non Callable ZeroCoupon if the curve is relative flat after the first call dateZero Accreting Swaps where the notional over which anannual coupon is paid increasesTo enhance the yield, the non-callable Zero Coupon canbe linked to a preferred credit (for example GE, Philips orBMW). In this case the investor sells default protectionon the selected entity for which he receives a premium.If the underlying entity defaults, the investor loses itsprincipal and will receive the unknown recovery value.This is a Credit Linked Zero Coupon Note

Example: Callable Zero Coupon Note

Currency EURMaturity 10 yearsIRR 3.75% (10Y rate 3.26%)Call NC1Y, annual afterwardsABN receives 6M EURIBOR -11bps or Notional

Delta profile of a 10Y Callable Zero Coupon Note

In the graph above the delta profile is shown. Asexpected, the main sensitivity is to 10 year interest rates. A decrease in the 10 year rate will increase themark-to-market value of the structure.


If rates increase, the relative mark-to-market of a Zerowill suffer as the fixed IRR will be lower than the prevailingmarket rate. If rates are stable or increase less than impliedby the forwards the Zero will outperform the benchmark.If rates decrease, the likelihood of the note being calledincreases and the investor will have had an above marketIRR but has to reinvest in a lower yield environment.

RisksZero Coupon Notes have a duration equal to its maturityand therefore have mark-to-market high interest ratesensitivity.

When the Zero Coupon Note is made callable, theinvestor is still exposed to reinvestment risk.

Also ConsiderBermudan Callable Note

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Attitude to Risk: Medium Aggressive


RisksAn unanticipated upward move of the chosen referenceindex can result in a low coupon or zero coupon structure(worst case scenario: 0.00% coupons and a value of thestructure close to the value of a Zero Coupon Note).

The structure is sensitive to absolute changes in ratesand implied volatility.

If the structure is callable the investor is exposed toreinvestment risk.


Also ConsiderTarget Redemption Note (since most Target RedemptionNotes are Inverse Floaters)Snowball

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Downward Shift

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(Callable) Inverse Floater

SummaryAn Inverse Floater suits an investor with the view that a certain index will stay low while the forward for thatindex is upward sloping. The coupon structure of anInverse Floater is a fixed rate minus a particular index,which therefore floats inversely with the chosen index.

Market ViewThe Inverse Floater suits an investor with the view that acertain index will decrease or stay low while the forwardfor that index is upward sloping. To support the view thatthe market is overestimating the future fixings, leverageis possible by subtracting a multiple of the index from ahigher fixed rate. Higher leverage provides greater potentialupside, but also increases the probability of reaching theworst case scenario: a 0.00% coupon. By choosing the extentof leverage the investor can express his risk appetite.

Description of ProductAn Inverse Floater is the opposite of a normal FloatingRate Note: rather than receiving the index, (a multiple of)the index is subtracted from a fixed amount. The lowerthe index resets, the higher the coupon. The mostcommonly used indices are short-term interest rates like6-month EURIBOR or 3-month USD LIBOR. Investorsgenerally floor the coupons at zero by buying a series ofcaps with a strike equal to the fixed amount divided bythe leverage. If the structure is Bermudan Callable, theinvestor has sold a Bermudan Swaption to the issuermeaning that he sold the right (but not the obligation) toredeem the notes at 100% on any given call date. As theinvestor sells the option, he prefers swaption volatility tobe high at inception (the investor is selling volatility).

VariationsThe index can be LIBOR, CMS, FX or the spreadbetween 2 indicesThe leverage can be set at a level which suits the riskappetite of the investorInverse floaters can be made (Bermudan) callable(Callable Inverse Floater Note)The index can fix in advance or in-arrears, whereby in arrearsfixing will take extra advantage of a steep yield curve

Example: Callable Inverse Floater

Currency EURMaturity 10 yearsCoupon 11.35% - (2 x 6M EURIBOR).

(At time of pricing 10Y Euro = 3.49%)ABN receives 6M EURIBOR - 11bps or NotionalCallable Semi annual

Delta Profile of a Callable Inverse Floater

In the graph above the delta profile of the CallableInverse Floater is shown. As expected, the investorprefers rates to decrease over all maturities.

Payoff Profile of a Callable Inverse Floater

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Example: Inverse Floater TARN

Type Guaranteed Inverse Floater TARNCurrency USDMaturity 5 yearsCoupon Y1: 6.00%, s.a. 30/360

Y2 - Y5: [13.50% - (2 x 6M USD LIBOR in arrears)]

ABN receives 3M USD LIBOR – 11bps or NotionalLifetime Cap 10%

Delta Profile of a GIF TARN

In the graph above the delta profile of the GuaranteedInverse Floater TARN is shown. As the structure haspossible automatic redemption in years 2 and 3, theinvestor prefers these rates to go down as the in-arrearsfixing is like a digital: a fixing at a level which will result in auto redemption or a fixing which will result in acontinuation of the structure.

GIF TARN Payoff Profile


Possible outcomes for a few volatility scenarios given

the GIF version

An increase in volatility increases the probability of higherinterest rates and thus a decrease in expected couponpayout which would result in a lengthening of the duration.The converse holds true for decreases in volatility. Althoughan increase in volatility also increases the probability oflower rates, in an upward sloping curve environment more“risk” is on the “higher rates” side.

RisksThe coupon payoff from target redemption structures issensitive to changes in the shape of the yield curve andvolatility curve.

The TARN has an unknown duration by nature, with in theworst case the final coupon (if the structure has a lifetimefloor, otherwise no coupon at all) on the maturity date ofthe note.


Also ConsiderSnowRange NoteCMS Spread Note (Flattener)

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Target Redemption Note (TARN)

SummaryA TARN suits an investor with the view that interest rateswill remain within a pre-defined band, or, as in the mostpopular structures, decrease over time (or increase lessthan implied by the forwards). The TARN automaticallyredeems when the total sum of the paid out couponsequals a designated target level (the Lifetime Cap) andtherefore has by definition an unknown duration. Althoughthe TARN can be seen as a feature (and implemented inmany products), due to its popularity we will describeTARNs as a separate product.

Market ViewThe TARN coupon structure can take several forms, but ingeneral the payout is designed to take advantage of stableor lower rates than implied by the forwards. The mostpopular structures are the Guaranteed Inverse Floater and the Guaranteed Ladder Inverse Floater. It is of coursepossible to structure the TARN such that it profits from anincrease in rates. With the Guaranteed Fixed Range Accrualvariant the barriers can be defined in such a way that theinvestor profits from increasing rates (by having a lowerboundary only). Obviously, the investor wants the durationof the product to be as short as possible (which will bethe case if his view proves to be correct) as the rate ofreturn is known per possible redemption date and decreaseswith time.

Description of ProductThe product derives its name from its embedded life timecap (sometimes referred to as the aggregate cap or min-max cap) and sets an absolute limit on the aggregateamount of coupon that will be paid over the lifetime ofthe structure. The sum of all coupons paid over the life of the transaction will be equal to the Lifetime Cap, andonce this target is reached, the structure automaticallyredeems. As most of the LIBOR based target redemptionstructures can potentially result in a negative coupon fora particular coupon period as well, most structures arefloored at zero. Also, in most structures the lifetime capis the lifetime floor: at maturity the final coupon pays anyremaining unpaid portion of the lifetime cap/floor (so the

structure has a minimum IRR). As such the product has an unknown duration. If interest rates and volatility fail torise or fall as much as implied by the forward curve thenthe duration of the trade can change significantly. In otherwords, the uncertainty of this product lies in the timingof the final payment and maturity.

VariationsThe TARN is available in those currencies where ABNAMRO operates underlying vanilla cap/floor and swaptionportfolios (in most currencies up to 10-years, in USD andYen up to 12-years and in Euro up to 15-years)The TARN payout may be a coupon bearing instrument orzero coupon and the coupon structure can be applied toalmost any coupon type that exists for a traded marketindex (a short term index such as LIBOR, a swap rate or an FX rate coupon). Currently, ABN AMRO offers thefollowing coupon types within the TARN structure:

> Guaranteed Inverse Floater (GIF): The coupon pays Max [Fixed Rate – (gearing x floating index), 0] up to the lifetime cap level, e.g. Max [X.XX% - (2 x 6M USD LIBOR in arrears), 0] subject to aggregate cap level of Y.YY%

> Guaranteed Ladder Inverse Floater (GLIF): The coupon pays Max [Previous coupon + X.XX% - (gearing x floating index), 0] up to the lifetime cap level

> Guaranteed Capped Floater (GCF): The coupon pays (Floating Index + spread) capped at X.XX% and subjectto the lifetime cap

> Guaranteed Fixed Range Accrual (GFRA): Fixed Rate x N/M (see Range Accruals)

> The Guaranteed SnowRange (GSR) combines the GFRA and a variant of the GLIF

> Hybrid Coupon: combines any of the coupon types described

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SummaryA Multi Index Note suits an investor with a specific viewon multiple markets or indices. By making the payoffdependent on two indices instead of one an investor canachieve a significant above-market yield if his view provesto be correct.

Market ViewMulti Index Notes are designed for investors looking foradditional yield pick-up and/or have a very specific viewon multiple indices and want to leverage this. An exampleis the Double Digital Option Note in which the digitalpayoff depends on two boundaries and two indices.

Description of ProductMulti Index Products have payoffs which depend onmultiple interest rates, multiple underlying indices or a combination of the two. Consequently, correlation is a consideration. In general, the investor prefers thecorrelation to be low at inception and increase over timeas most investors prefer selling out-of-the-money options.Low correlation increases the likelihood that the twoindices will breach a certain constraint, and therefore theupfront pick-up for the investor is higher. After trading, if correlation increases, the likelihood of the two indicesbreaching a certain rule falls, since they move more inline. Therefore the note becomes less risky for the investor,which will have a positive effect on the mark-to-market ofthe structure (the investor is said to be “long” correlation).Since the investor usually sells out-of-the-money options,he prefers volatility to be high at inception but to decreaseover time, as an out-of-the-money option with decreasingvolatility has a smaller likelihood of becoming in-the-money.

VariationsDifferent underlying indices are possible such as(quantoed) money market rates, swap rates and FX ratesDouble Digital Option: the digital pay-off depends on 2boundaries and 2 indices. For example the client receives9.00% if 3M USD LIBOR fixes below X.XX% AND 10YUSD CMS fixes above Y.YY%Linear Trigger Option. For example the client receivesUSD 10Y CMS + 35bps if (10Y CMS - 2Y CMS) > 0.Dual Range Option: the investor will receive a fixed orfloating payoff if 2 conditions are met. For example theclient receives a coupon of X.XX% x N/M for all days 3MUSD LIBOR is within (2.50% - 6.00%) AND USD/JPY iswithin 90.00 - 120.00).

Example: Double Digital Range Accrual

Currency USDMaturity 5 yearsCoupon 9.50% x N/MN number of days CMS 2Y > 4.50%

AND CMS 10Y - CMS 2Y > 0.00%M Total number of daysABN receives 3M USD LIBOR or Notional

Multi Index Note

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Delta Profile of a Double Digital RangeAccrual

In the graph above the delta profile of the Double DigitalRange Accrual is shown. As expected, the structureprofits from increasing rates and a steepening of thecurve. The negative delta in year 5 is partly due to thenotional effect, since it is a 5-year note.


RisksA bet on multiple indices will result in a higher probability ofreceiving a zero coupon. The worst case is a consecutivebreach of one of the barriers resulting in 0.00% couponsand a value of the note close to the value of a ZeroCoupon Note.

The investor is exposed to more complex (and less observable) sensitivities.


Also ConsiderHybrid Coupon TARNDynamic Cap

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A parallel shiftupwards ora steepening ofthe yield curvewill normally bepositive for thestructure.

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SummaryA dynamic cap suits investors with a view on the slope of the yield curve or on the difference between 2 rates in different currencies, and is a variant of the well knownspread option. This variable strike cap can be added to astructure in order to finance the extra leverage sometimessought. So instead of having a cap fixed at 7.00%, the capis at 3M USD LIBOR + 100bps; hence, it is “dynamic”.The coupon therefore depends on the minimum of 2payoffs: the leveraged difference between 2 indices andan index plus a margin.

Market ViewSelling a dynamic cap gives the investor both a relativerate view (i.e. an intra-curve or inter-curve) and a view onthe absolute level of interest rates. For example, if a curveshifts upwards and also steepens, the dynamic cap strikeincreases and avoids a negative impact on the payout ofthe steepening as opposed to a fixed cap. Selling thevariable cap enables the investor to finance the leverageon the Spread. An example payout is a note which paysthe minimum of a weighting times an index, plus a spread(for example: 3M USD LIBOR + 100bps), or a leverageddifference between 2 indices (for example: 10 x (10Y CMS– 2Y CMS)). Without the dynamic cap the leverage wouldhave been lower, for example 8 x (10Y – 2Y). The structureis often floored at 0.00% (always in note format), and theinvestor generally profits if the curve steepens or a spreadwidens (in the case of a spread on 2 rates in 2 differentcurrencies) and the 3rd reference rate shifts upward.

Description of ProductThe dynamic cap product is an enhancement of thespread option structures capped at a fixed rate: theinvestor is selling a variable cap on a spread of 2 rates(single or multi-currency). The variable cap depends on one of the 2 indices in the spread or a third index.Typically, the investor buys a spread option to floor thestructure. Furthermore, when the curve is flat (or the

spread between the 2 rates in 2 different currencies is low) the dynamic cap investor is long volatility on thespread at inception. He prefers low volatility at inceptionto reduce the cost of the floor, but prefers high volatilityafter trading, as it raises the likelihood that the spreadwill widen.

VariationsA guaranteed minimum coupon can be achieved, althoughthis decreases the upsideThe absolute coupon can be capped, increasing theleverage over the spread or margin over the single indexA flattening view can be accommodated. However, incurrent market conditions the floor will be expensive tofinanceA fixed rate can be added to the leveraged Spread (forexample Min (3M + 1.00%, 2.00% + 5 x (10Y – 2Y))A Dynamic Floor can be structured (for example Max (3M– 1.00%, 6 x (10Y – 2Y)), floored at 0.00%

Example: Dynamic Cap

Currency USDMaturity 5 yearsCoupon Y1 - Y2: 8.00%

Thereafter : Min [3M USD LIBOR + 1.00%, 10 x (10Y CMS – 2Y CMS)]floored at 0.00%

ABN receives 3M USD LIBOR or Notional

Dynamic Cap Note

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Delta Profile of a Dynamic Cap

This graph shows the delta profile of the Dynamic Cap.As expected, the investor profits from a steepening ofthe curve. The structure overall has a slightly negativedelta due to the notional effect, the floor at 0.00% andthe fixed element in the cap. A structure with a fixed capwould have a higher negative delta. The high negativedelta in year 5 is partly due to the notional effect: it is a 5 year trade.

Sensitivity to Rate MovesOverall, the structure benefits from a steepening of thecurve. Although the structure has limited parallel shiftexposure, a parallel upward shift will be slightly negativefor the structure due to the notional effect, but slightlypositive for the structure if it is combined with a steepeningof the curve. A steepening of the curve implies higherforward rates and thus a higher forward cap. The advantageof a dynamic cap over a fixed cap in a parallel upwardshift is therefore obvious: a parallel upward shift won’timpact the absolute coupon level. The structure is moreattractive when at inception the forward curve is flat.

RisksThe main risk will be with the underlying payoff which iscapped by the dynamic cap (worst case scenario: 0.00%coupons and a value of the structure close to the value of a zero coupon bond).

A Flattening of the curve will have a negative impact onthe mark-to-market of the structure.


Also ConsiderCMS Spread NoteMulti Index Note

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Attitude to Risk: Medium

SummaryThe Volatility Note suits an investor with the view that thevolatility of a particular index will go up. A Volatility Notepays a coupon which is linked to the absolute variation ofan index over a set period of time. The more variation, thehigher the payout will be.

Market ViewA Volatility Note suits an investor with the view that thevolatility of an index will go up. The investor takes advantageof any movements of the index, without having to take aview on the direction of the index. The note can also beused as a hedge for long term bond investors whoseportfolios have natural negative volatility.

Description of ProductA Volatility Note paying an annual coupon of (gearing xthe absolute change of an index) is similar to being long astring of cash-settled one-year swaption straddles, resetat-the-money every year. The investor is therefore said tobe “long Vega”: he profits from an increase in volatility. Amajor advantage of the Volatility Note is the fact that theinvestor can play the absolute variation of an index, withoutthe complexity of managing a rolling option position.

VariationsThe Volatility Note can be made digital: if Index X inarrears – Index X fixes at or above Y.YY%, the investorreceives a fixed coupon. Otherwise no coupon is paidThe note can be constructed as an inverse floater,profiting from a decrease in volatilityInstead of one index, two indices can be used

Example: 10Y Digital Volatility Note

Currency EURMaturity 10 yearsCoupon 5.25% if |10Y CMS in arrears - 10Y

CMS| > 0.40%, annual 30/360Fixing Annual, 2 bd before coupon paymentABN Receives 6M EURIBOR + 8bps or Notional

Delta profile of a 10Y Volatility Note

In the graph above the delta profile of the 10 year digitalVolatility Note is shown. The negative delta in year 10 is thenotional effect: it’s a 10-year note. The longer maturitybuckets indicate a preference for increasing rates which islogical as the 11 year rate can be seen as the 10 year rate1 year forward, which the investor obviously likes to increase.Overall the investor prefers a steepening of the curve.


RisksA decrease in volatility will result in a below-market orzero coupon (worst case are consecutive 0.00% couponswith the value of the structure close to the value of a ZeroCoupon Note). When transacted in note form, the notemay trade below par during the life of the transaction.

Also Consider(One Look or Multi Look) Digital Note

Volatility Note

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SummaryA Bond Discount Note (BDN) suits an investor with theview that a reference bond (typically a government bond)will stay above a certain strike level (a certain price). Theinvestor receives his money back if the fixing is at or abovethe strike (the preferred scenario: cash settlement) orreceives the underlying bonds at a higher price than thespot price of that bond (bond delivery, resulting from afixing below the strike). A BDN is mostly a short term play.

Market ViewThe buyer of a BDN should have the (short term) viewthat rates stay stable or decrease slightly (or increaseless than implied by the forwards), because with a largefall in rates he would prefer to buy the underlying bond.

Description of ProductWith a BDN, the investor sells a put option on a bondwith a certain strike to the issuer, obliging the investor to buy the underlying bond at a predetermined price anddate if the buyer of the option (in this case ABN AMRO)wishes to sell. For this the investor is compensated by an option premium, paid as an above-market coupon. Inorder to maximise the coupon it is important for the BDNthat the reference bond’s coupon is not too high, and thebond does not have too many accrued days of interest.This would reduce the Participation Level. If at maturitythe option is in-the-money, the underlying bonds aredelivered “dirty” (with accrued interest). A relatively highcoupon and accrued interest leads to a relatively higherdirty price, therefore reducing the number of deliverablebonds per denomination. Hence the upfront premium willbe lower. High volatility at inception is positive for theinvestor as the option sold has more value and thereforeincreases the coupon. A Bond Discount Note is alsoknown as a Bond Reverse Convertible. The structure is not capital guaranteed.

VariationsThe maturity can range from 3-months up to 2-years in allcurrencies and government bonds for which ABN AMROoperates an option marketThe strike can be based on a certain coupon requirement,or the coupon can be based on the investor’s strikepreferenceInstead of government bonds the investor can select acorporate bond. By selecting a corporate bond the maturityhas a maximum of 6-monthsIt is possible to structure a BDN in which bond delivery is the preferred scenario and cash settlement the nonpreferred one (for example cash settlement at a lowerlevel than 100%)This structure is also very popular on FX (called DCD’s:Dual Currency Deposits) or Equity (Reverse Convertibles)

Example: Bond Discount Note

Currency EURMaturity 3 monthsCoupon 4.75% (3M EURIBOR at 2.17%)Underlying Nether 3.25% 2015Strike 100.50% (at time of pricing 100.71%)

If fixing is at or above 100.50%, the investor receives thecoupon and the note will be settled in cash (the investorreceives his money back). If fixing is below 100.50%, theinvestor will receive his coupon, but settlement will be inbonds: the investor receives a number of the referencebonds instead of his money back.

Bond Discount Note

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Delta Profile of a Bond Discount Note

The delta profile shows that the sensitivity is obviously to the long rate. If rates decrease the price of a fixedincome instrument will increase so the probability ofdelivery of the underlying bond will decrease (as the spot price will move away from the strike price).

If rates increase the probability of the strike beingtriggered at the maturity date increases.

As the structure involves selling a put option, there issome mark-to-market sensitivity to volatility.


RisksA fall in the price of the underlying bond can result indelivery of the bond at a higher price than the presentmarket price (not a capital guaranteed structure).

Also ConsiderOne Look Digital NoteD

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Most Popular Products

Structured Note Market

Turbo Certificates

Interest Rate Models

Modelling Processes

Yield Curve Considerations

Appendix

SummaryInterest Rate linked MTNs still hold the major share ofthe structured MTN market, with a wide and growingvariety of structures.

Despite the difficult market conditions, CMS structuresstill have a large market share (11% of YTD MTN issuance).However, the progression made within interest-rate linkedMTNs has been significant. The numerous innovativestructures developed within the sector have diversifiedinvestors’ interests. In the first quarter of 2006, 130different structure variations have been issued comparedto 163 in all of 2005. This said, the traditional pay-offs stillremain the most trusted and hence most popular.

2006 1st Semester Interest Rate Linked MTN Split

Source: mtn-i.com.

CMS StructuresThe CMS structure has been hugely popular in the pastfew years, with particularly explosive growth in 2005, whenalmost 25% of all MTN’s were CMS-linked to some extent.The change in clients’ views since the period of short-endinterest rate hikes, and of course heavy curve flatteningon both sides of the Atlantic has meant this share hasmore than halved to 11% YTD 2006.

2006 1st Semester CMS Breakdown

Source: mtn-i.com.

The graph above shows the breakdown of the mostpopular MTNs with a CMS underlying element.

The standard CMS Linked MTN (where returns are basedon a constant maturity swap reference rate) decreased inpopularity but was still heavily represented in the market,making up 12% of interest rate linked issuance YTD 2006,down from 21% in 2005 (by USD equivalent value).

In recent years, a popular structure has been the additionof leverage to the CMS Spread Note: a note offering abovemarket returns if the investor’s view on the spread betweentwo swap rates proves correct. As mentioned, the growthhas been largely driven by investors positioning themselvesfor a steepening of the yield curve.

CMS Spread Range Accruals remained popular, at 6% ofYTD 2006 Interest Rate linked MTN issuance. This structureallows investors to accrue above market returns for everyday the spread between two reference rates fixes withina defined range. These are digital structures and are usuallystructured to allow investors to position themselves fornon-inversion or steepening of the yield curve.

Most Popular Products

Range AccrualStandard CMS LinkedCallable Zero couponCMS Spread Range AccrualBermudan CallableAccreting ZeroFlipperFixed Rate CallableFixed Rate Step-Up CallableInverse FRNEuropean CallableCapped Floating Rate NoteTarget Redemption NoteOthers

22%12%8%6%5%5%4%4%3%3%2%2%2%

22%

Standard CMS LinkedCMS Spread Range AccrualCMS SpreadCMS Volatility LinkedCMS Linked Range AccrualCMS Linked QuantoCMS Linked Target Redemption

54%25%10%4%4%2%1%

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Range Accrual NotesThe standard Range Accrual structure accrues interest forevery day that the reference rate fixes within a predefinedrange. The standard version remains a popular structure,accounting for 10% of overall MTN issuance YTD in 2006.The range accrual feature is increasingly used in moreexotic varieties: for example cumulative coupon, flippableand target redemption.

USD Range Accrual issues have fallen. USD issuanceaccounted for 80% of all Range Accruals in 2004, 67% in2005 and now down to 33% YTD 2006. Investor demandfor USD denominated issues has fallen amidst the prolongedFed Funds tightening cycle, leading to concern about ratesbreaking out of the predefined range. The demand wasfurther lowered by continuing USD weakness.

Callable & CumulativeCallable MTNs are notes where the issuer has the optionof early redemption. In 2004, 31% of all Interest RateLinked MTNs were callable, compared to 19% in 2005and back up to 24% in 2006 YTD (by USD eqv. value).

Main Callable Structures - 2005 vs. 2006 (1st semester)

Source: mtn-i.com.

The main conclusion to be drawn from the graph below is that relatively vanilla structures, such as the fixed rateand zero coupon callables, have gained market share in2006 so far. The Zero Coupon Callable Note is finding itsplace in the market due to the higher IRR on offer, madepossible through the higher yield curve environment.Similarly, fixed rate issues now look more attractive aftera period of rate hikes in Europe and the US.

Similarly, there has been a fall in activity of cumulativestructures, whereby the payout of each coupon is “pathdependent” – reliant on the level of the previous coupon.In 2005, 4.5% of all issuance had a cumulative element,falling to 1.9% in the first half of 2006 (by value).

In summary, the overall change in activity in the MTNmarket can be attributed to market conditions that affectthe risk appetite of investors, as well as issuers delayingissuance until there is more confidence in the market.

InnovationWith H1 06 interest rate-linked MTN sales down by USD51bn on H1 05 and the Euro and US dollar yield curvesuninspiring, rate structure buyers seemed to have movedaway from some of the heavily structured IR-linkedinstruments that were popular in 2005. Hybrid productson the other hand have seen a significant increase involume, notably those that combine interest rate playswith inflation exposure.

In just the first eight weeks of 2006 hybrid issuance hadalready overtaken 2005’s volume. This underlines theemergence of an important new product tailored to aspecific set of risk preferences. Many of these structurestend to exploit the behaviour of the forward EURIBORcurve versus the forwards for Eurozone HarmonisedIndex of Consumer Prices (excluding tobacco; HICPx). The majority pay a floating rate plus a spread capped at a multiple of the HICPx and floored at 0%.

The interest rate-linked MTN market has responded bydelivering bespoke solutions to investor demands andhas adapted its offering to the changing rate markets.

Innovation is clearly the driving factor behind the market.Within Interest-Rate linked MTNs alone, the number ofproduct variations issued per year has risen from 42 in2001 to 163 in 2005. 130 different structures have beenissued during the first quarter of 2006 and the fast-pacedand bespoke nature of the market means this figure issure to reach 200 by year end.

Furthermore, the contribution of the ten most popularstructures to total IR-linked issuance has shown a steadydecline since 2002. Added to the speed of product take-up, it makes flexibility and responsiveness crucial formarket participants. See graph.

Interest Rate Linked Product Innovation

Source: mtn-i.com.

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FX-linked MTNs showed a significant sales surge with almost a four-fold increase from USD 1.4bn in Q4 05 to close to USD 5bn in Q1 06. This supply was driven by investor appetite for exposure to emerging marketcurrencies. The largest ever FX-linked MTN was an Asiancurrency basket, whilst the most dominant currencieswere the Chinese renminbi, Indian rupee, Indonesianrupiah and Korean won.

The Credit-linked MTN market has shown one of thestrongest recoveries at the start of the year, but, perhapssurprisingly, commodity linked MTNs have not taken off(only USD 1.1bn of new issuance in the first semester).

OutlookInterest rate linkers look set to remain the dominantasset class, although the difficult environment for CMSbased structures has also shifted the focus to differentasset classes. Amid investor uncertainty about marketdirection, a revival in simple callable structures hasemerged. Ratchet Notes, Capped FRNs and zero accretingnotes have also been gaining in popularity. This trendtowards relatively straightforward structures is expectedto continue in the near future. The inflation capped FRNhas been the year’s major development; appetite for theseand other inflation-linked structures should continue to bestrong with continuing inflation fears in both Europe andthe US. Another factor that might drive the market is thecontinued development of hybrid structures linked tomultiple assets and markets. This has greatly enhancedinvestment possibilities. Lastly, Japan’s departure fromthe zero interest rate policy offers new opportunities,particularly for Asian investors.

SummaryAlthough lower than last year’s record figures, structuredMedium Term Note (MTN) issuance appears to be strongin 2006 with year-to-date issuance of USD 94bn. 2005 sawextremely strong issuance in the first quarter, followed bya slight downturn thereafter. Strong issuance at the startof the year is a trend that is often observed, amid stronginvestor appetite and fresh issuer funding targets. Thiswas also the case at the start of 2006, with a strong pick-up in issuance over Q4 2005. As could be expected in anenvironment of booming equity markets, equity linkedstructures have gained in market share. Having said this,despite difficult bond market conditions, interest ratelinkers still dominate the issuance with a market share of48%. The recent Euro strength has also led to an increasein Euro issuance (50% of the market) and a decline inUSD denominated structures (29%).

Structured MTN Market Size

Source: mtn-i.com.

Market SectorsInterest Rate Linked issues continue to dominate thestructured market at 48% of YTD new issuance (USD45bn), although it is lower than in 2005 as investors’interest has shifted to a wider variety of asset classes ina difficult interest rate environment. CMS-linked structureshave so far been less popular than in 2005, brought onprimarily by the severe flattening of the yield curve.

The high returns observed in stock markets have led to increasing equity linkage (22% of YTD deal volume), showinga significant increase from 14% in 2005. Issuance doubledfrom H2 05 to almost USD 21bn in H1 06.

Investors are once again looking for real returns throughinflation linked products. The rebound in volume in Q1 06to USD 5bn equalled that across all of 2005. Innovativehybrid inflation products drove more than 50% of Q1 06sales in this asset class. In particular, the inflation cappedFRN accounted for most of these. It is a simple yieldenhancing structure that exploits the correlation betweenthe forward EURIBOR curve versus the forward HICPx curve.Pure inflation sales were dominated by HICPx (Eurozone)and UK RPI. Spanish and, for the first time, Polish inflationalso featured. Q2 06 has begun with leveraged cross-marketdifferential notes referencing local and pan-Europeaninflation.

Structured Note Market

Q2 Q2 Q2 Q2 Q2 Q2 01 02 03 04 05 06

Interest Rate LinkedEquity and Equity Index LinkedCurrency LinkedOther (Credit, Commodity, Hybrid, Fund, Bond Linked)Total Issuance

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SummaryTurbo Certificates (“Turbos”) are delta-one investmentinstruments which give investors leveraged exposure toan underlying bond future. Depending on whether theinvestor has a bullish or bearish view on interest rates incertain maturities and geographic regions, he can chooseto buy a Turbo Long or Turbo Short. Turbos on bond futuresare defined by their underlying future, the financing leveland stop-loss level.

Market ViewAn investor can use Turbos to take an aggressive view ona certain bond market. If he expects sharply rising longterm interest rates in Japan for instance, he can buy aTurbo Short on the JGB future. Equally, an investor whoanticipates declining long term rates in Europe canchoose to buy a Turbo Long on the Bund future.

Equally, Turbos can be used to hedge interest rate risk ina bond portfolio. Because Turbos always reference thefirst maturing futures contract, their interest rate sensitivityis relatively constant. This allows an investor to match theduration of his bond portfolio with a required amount ofTurbos. The hedge achieved in this way will never be perfect,as it will for example not necessarily protect against changesin slope of the yield curve, but it is easy to implement andrequires little capital outlay.

Description of ProductA Turbo is designed to offer one-for-one exposure to theprice changes of the underlying future. A 1 EUR increasein the price of the underlying contract should lead to a 1EUR price increase of the relevant Turbo (not accountingfor fees).

The price of a Turbo is equal to the difference between the market price of the underlying future and the financinglevel of the Turbo. The financing level can be seen as theamount of money that ABN AMRO has to contribute tobuy the underlying above the premium paid by the investor.Because the underlying is a future (not a physical asset)in this case, ABN AMRO does not physically have to“lend” money to the structure. This means that nointerest is charged over the financing level; however, the management fee does accrue over this amount.

The stop-loss level is slightly above the financing level inthe case of a Turbo Long, and slightly below the financinglevel in the case of a Turbo Short. If the underlying futurehits the stop-loss level, the Turbo ceases to exist andABN AMRO unwinds the position. Depending on marketcircumstances, the investor will then receive the residualvalue of the Turbo, which can never be smaller than zero.The stop-loss level is determined by ABN AMRO, and islargely dependent on the volatility of the underlying market.

As Turbos will always reference the first maturing futurescontract, ABN AMRO periodically rolls the underlyingcontract. On a roll date, the price of the next maturingfuture will not be the same as the price of the currentfuture. To keep the price of the Turbo constant during therolling process, the financing level is adjusted to accountfor the price difference between the two futures contractsand any costs incurred during rolling.

Turbo Certificates

Example

Type Turbo LongCurrent Underlying Future Euro-Bund Future Sep. 2006Price of Underlying 116.80 EURFinancing Level 104.14 EURStop-Loss Level 106.27 EURFair Value Turbo 12.66 EURLeverage 9.2 (Price of Underlying/Price

of Turbo)Management Fee 1.5% p.a., accrued daily over

the Financing Level

UnderlyingsTurbos Long and Short are currently offered on thefollowing Bond Futures:

Europe: BOBL, Schatz, Bund, BUXLUnited States: T-Note, T-BondJapan: JGB

RisksTurbos are highly leveraged investments, which meansthat buyers risk losing their entire invested capital.

A stop-loss event will result in the position beingunwound and the investor receiving the residual value,which is dependent on market circumstances and couldbe zero.

An interest rate hedge using Turbos may not be perfect.

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BackgroundIn the last twenty years interest rate sensitive productshave become increasingly popular. The values of thesesecurities are closely related to the shape and the apparentlyrandom movements of the term structure. Therefore,numerous models have been developed to simulate thefluctuations of the yield curve.

Unlike other asset classes as equities and foreign exchange,where the Black-Scholes framework is universally acceptedto determine the price of derivative products, no suchagreement exists with regard to interest rate modelling.The event being modeled (the fluctuation of interestrates) is much more complex than the movements of an index price and so three generations of interest ratemodels have evolved.

The first generation proposed to model the interest ratedirectly starting with the nearest maturities (short end):the short rate models. The second generation modelscomprise the Heath-Jarrow-Morton (HJM) models whichattempted to model the forward curve directly. The latestgeneration are market models. The LIBOR specificationof these models is also known as the Brace-Gatarek-Musiela (BGM), who were amongst the first to publish it.BGM attempts to model the forward rate curve startingwith market observable forward rates.

Common ThemesUnderlying all three generations of models, a stochasticdifferential equation describes the yield curve. Theevolution of modelling has come about through differingways of describing the yield curve (using spot or forwardrates) and the complexity of adjustments for time, volatilityand correlation.

The essential assumption of believing the markets to bearbitrage-free and complete (all risks can be hedged out)allows the market price of risk to be removed. The valueof a derivative is simply the replica costs and thereforeindependent of the risk appetite of the investor.

To use any model for pricing, it must be calibrated to the market. Besides matching the initial yield curve, theprices of caps/floors and swaptions are required (veryliquid securities). Ideally the model is capable of providingan analytical formula for these vanilla instruments, butotherwise a very efficient numerical algorithm is necessary.Spot and forward models must derive the appropriatecalibrating quantities from market observable rates. Byconstruction, market models are based on observablerates in the market and hence readily price-standardinstruments.

The first generation of models developed were generallyspot rate based, in which the entire yield curve is specifiedby a single variable. This choice was due to a combinationof mathematical convenience and numerical ease ofimplementation.

Short Rate ModelsBy short rate here, it is the rate that is observed for theshortest-term loans starting at a certain point, borrowingnow and repayment after a small time interval (i.e. asecond, minute or even a day). The model is characterisedby the exact specification of the spot rate dynamicsthrough time. The simplest short rate models are rarelyused in practice as they have few parameters and noability to calibrate to the entire yield curve. The basicmodel implies that all rates move in the same directionover a short time interval, but not all by the same amount.Parallel shifts are possible and steepening or flattening aswell only when the relative shift along the curve varies inthe same direction.

The later model engineered by Vasicek is more commonin this category as it incorporates the concept of meanreversion. Mean reversion is the tendency to revert backto some long-run average level over time. That is if ratesare observed much higher than the long-run average, it ispulled back to that average and vice versa for lower rates.

Interest Rate Models

An extension of Vasicek is the Hull-White model that correctly reproduces the initial entire yield curve andincorporates time dependant mean reversion. This model still leads to explicit formulas and can be used toanalytically price caps and floors, however valuing thesevanilla instruments is useful primarily for calibration. Thereal use of the model is to value more exotic optionssuch as Bermudan Swaptions.

Forward Rate ModelsThe Heath, Jarrow & Morton (HJM) model, in contrast tothe spot rate approach, models the entire yield curve by,in small time stages, changes to the forward curve. Bytaking the initial forward rate curve as given, the HJMmethodology directly models the entire term structure of forward rates. The HJM model permits more than onefactor to influence the forward rates: it can have morethan one source of volatility.

An important feature of the HJM model is that it permitsinterest rate volatility to change across time: though it is difficult for the user to specify how volatility changesthrough time. Moreover, it gives the model characteristicssimilar to the Black-Scholes model, used to price optionsfor other asset classes. It takes the price of the underlyingasset, the term structure, as given, and requires knowledgeof the volatility of the underlying. Heath, Jarrow and Mortonsuggest several functional forms for the volatility of theterm structure, such as letting volatility exponentially dampen,meaning that it decreases proportionally with time.

Due to the time dependency and flexibility, the model is computationally intensive although it allows for moresophisticated and consistent pricing. HJM models requirethe use of a Monte Carlo Simulation, a procedure thatrandomly samples changes in market variables by runningthe model repeatedly (10,000 or more) and taking theaverage result.

Market ModelsThe motivation for the development of market modelsarose from the fact that, although the HJM framework istheoretically appealing, its standard formulation is basedon unobservable instantaneous rates. These rates aretherefore fundamentally different from actual forwardLIBOR and swap rates, as traded in the market.

Market models can be used to price any instrumentwhose pay-off can be decomposed into a set of forwardrates, and is commonly used for exotic interest ratederivatives such as a Bermudan Swaption and a CallableRange Accrual. Each forward rate has a time dependentvolatility and time dependent correlation with the otherforward rates being evolved. After specifying thesevolatilities and correlations, an instrument can be pricedusing Monte Carlo simulation to evolve the forward rates.

The match to the market Black pricing formula (1976) foroption prices makes calibration of market models verysimple. The quoted implied Black volatilities can directlybe inserted in the model, avoiding the numerical fittingprocedures that are needed for the spot rate or forwardrate models. They have the advantage when calibrating to their associated vanilla product (i.e. a LIBOR model forcap products) in allowing a separate fitting to volatilityand correlation, since the formulation of this category of model allows a decoupling between the two.

ConclusionThe three generations of interest rate term structuremodels, by virtue of being arbitrage-free, are equivalentmathematically and are all within the general HJMframework. Each is distinguished by different methods of constructing the effective volatility function whichdetermines its use in practice.

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BackgroundThe pricing of any derivative product is dependent on the (expected) future price of the underlying asset. Whenmodelling asset price movements over a period, a numberof models have been associated with the process drivingthe numbers. Asset prices, like molecules, are oftenassumed to follow Brownian motion, which is an extensionof the ideas discussed on where a “drunkard” might endup after some time on their walk home.

The value of a derivative is the value today (present value) of all expected discounted cash flows. The expecteddiscounted cash flow is basically the probability of receivingthe cash flow times the expected payout, conditional onreceiving the cash flow (i.e. in option terms, receiving theexpected payout conditional upon the option being in themoney). For this reason numerous models have attemptedto model price movements to value derivative instruments.

The ProcessesTo understand how asset prices can be modelled, anunderstanding of the variable (price) is first required. Anyvariable whose value changes over time in an uncertainway is said to follow a stochastic process: the variable isneither completely determined nor completely random as it contains an element of probability. The example ofrolling a dice at regular time intervals shows that rolling a “6” three times in a row does not mean a 6 will not berolled again, however, intuitively it is quite unlikely. Thismeans that after a large number of sequential throws(with a “fair” dice), we expect to see each number anequal number of times, though might see a “6” rolled four times in a row.

An extension to this idea introduces a Markov process,which is a particular kind of stochastic process. Its propertyis that only the current value of the dependent variable(i.e. the asset price) is relevant for predicting its next value.In other word it has “no memory”: the asset price pathleading to its current value has absolutely no influence or effect on what the next asset price movement will be.

More technically speaking, a Markov process is consistentwith the “weak” form of the efficient market hypothesis.Historical asset prices are not of any use in predictingfuture prices; therefore it is impossible to produceconsistently superior returns through technical analysis.

Stochastic processes can be classified as discrete orcontinuous time. A discrete-time process is one wherethe value of the variable can only change at certain fixedpoints in time, whereas a continuous-time process allowsfor a change at any time. The same breakdown can beapplied to the variable that the process is modelling, inthis case, the asset price. In a continuous-variable process,the underlying variable can take any value within a certainrange; whereas in a discrete-variable process, only certaindiscrete values are possible. In practice, asset prices arerestricted to discrete values (e.g. multiples of a cent) andchanges can be observed only when the exchange is open.

The Random-Walk ProcessThe foundation for asset price modelling is the “RandomWalk”. It is the intuitive idea of taking successive steps ina random direction for modelling stochastic processes. Itis called a random walk because it can be thought of asan individual (drunkard) aiming to walk on a straight lineto a chosen destination, who at each point of time cantake one step to the right with a given probability p orone step to the left with probability 1-p.

The simplest random walk is a path constructedaccording to the following rules:there is a starting pointthe distance from one point in the path to the next is aconstant (constant footsteps)the direction from one point in the path to the next ischosen at random, and no direction is more probablethan another (the drunkard is just as likely to slump to the left as to the right)

Modelling Processes

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Suppose we draw a line some distance from the origin ofthe walk to the intended end point. For any random walk,every point in the domain will be crossed a number of timesalmost surely. The graph below shows eight random walksof 100 time steps, each aiming to go straight across.

An important result that follows is the deviation from theintended straight line (variance) of a random walk increaseslinearly with time. An individual walker strays further awayfrom the intended straight line with time. If the whole pubwere to attempt the same walk, the average position awayfrom the line would indeed be on the line at each point.

8 random walks aiming to go straight across

The motion analyzed is called a Simple Random Walk. It issimple in the sense that the walker makes discrete fixedmovements of constant lengths at specified time intervals.The Wiener process develops the principle to asset pricingsuch that prices do not move by a constant amount in agiven period but are influenced by a driving variable: anumber generated to influence the relative price shift.

Wiener ProcessA Wiener process puts a mathematical probability and rangeconstraint upon the driving variable. It is still randomly generatedbut conforms to a normal distribution with a mean of 0 (drift)and a standard deviation of 1 (variance). This means that abouttwo-thirds of the time, the number will be between +1 and -1,or one standard deviation around the average of zero. About95 percent of the time, the numbers will be between twostandard deviations of the zero and 99 percent of the time,they will be between three standard deviations of zero.

The industry-standard GBM (Geometric Brownian Motion)equation relates the new asset price to the old one througha time dependent term and a random variable. Whensimplified for the Wiener process, the random variable isthe product of the driving variable, described above, andthe square root of the time interval. Essentially a modeluses the volatility and expected return at each time intervaland the amount by which the price moves is determinedby the random number. It has a deterministic element(the expected return/drift) and a random term (which ismore or less important dependent on the volatility). Dueto the characteristic of the Markov process, the pricechart will vary considerably each occasion the model isrun. A Monte Carlo simulation of the stochastic processis required to sample the random driving variable andderive the price chart. The simulation runs the modelrepeatedly (often 10,000 times) and takes the averageresult. If the model were to be adapted for continuoustime, the model describes geometric Brownian motionwhich is the basis of the Black-Scholes model. As discussed,the return to the holder of the stock in a small period oftime is normally distributed and the returns in two non-overlapping periods are independent.

ConclusionWhen pricing derivative products, to avoid overcomplicatingthe process, an understanding of the modelling behind theunderlying asset pricing is essential. The “random walk”of asset prices includes a number of simple assumptionscombined together:the price is derived from the previous one but does notaffect the result (Markov)the annual expected return should depend on the risk ofthe return on the assetthe annual volatility needs to be carefully chosenthe Wiener process provides the basis for the randomnature of the price

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SummaryThe Yield Curve, also known as the Term Structure ofInterest Rates, is the relationship between yields andmaturities for a given security. Its shape and absolutelevel are of vital importance to investors, and an array ofstructured products makes it possible to link returns toany view on the future movements of the curve. Whereparallel shifts express current rate moves, the slope isabout expectations of future moves.

Main TheoriesThe main considerations of the yield curve are its level,slope and curvature. Typical shapes of the curve include:“Normal” (upward sloping); “Flat” (horizontal); and“Inverse” (downward sloping). The curve may also be“humped” (see graph below).

Hypothetical Yield Curves

There are three dominant theories which attempt toexplain the term structure of interest rates:

Pure Expectations Theory: According to this theory, the forward rates (interest rates between two future dates)implied by the yield curve are pure expectations of futureinterest rates. An upwards sloping yield curve environmentreflects the expectations that interest rates will rise; a flatcurve implies that interest rates will stay broadly constant;and a downward sloping curve implies falling interest rates.The main shortfall of this theory is that no considerationis given to the inherent risk associated with investing forlonger maturities.

Biased Expectations Theory: This theory suggests that whilst the forward rates do reflect interest rateexpectations, they also contain a risk premium. TheLiquidity Preference Theory proposes that investorsprefer to retain liquidity by holding short term securities,whereas borrowers prefer to borrow for longer periods,giving the yield curve an upward bias. The PreferredHabitat Theory agrees that a risk premium is reflected in forward rates. However, this theory suggests thatinvestors and borrowers have different maturity preferences,and are willing to switch away from their “preferredhabitat” maturity if sufficiently rewarded.

Market Segmentation Theory: Like the Preferred HabitatTheory, this theory suggests that different marketparticipants have differing maturity preferences. However,the Market Segmentation Theory does not allow for anyswitching between “segments” (areas of the yield curve),and therefore the yield in any segment is independent of other sections of the curve. Most market participantsagree that this theory offers a rather dubious explanationof the yield curve.

Supply and Demand90-95% of yield curve movements are accounted for byparallel shifts in the curve, and the debate over whichtheory explains these movements continues. However,the supply and demand factors influencing the yieldcurve environment warrant consideration:

Supply Side FactorsCentral Bank monetary policy is arguably the mostimportant determinant of the yield curve, certainly in the short term. The direct effect of Central Bank ratemovements is to alter supply conditions at the very shortend of the yield curve. Although the main effect would bea parallel shift in the yield curve, it is possible that theremay be an impact on the slope as well: a rate tighteningcycle would have a larger impact on short term interestrates, driving them higher than less sensitive long termrates. This flattening could be compounded by the laggedeffect a rate hike might have on inflation: lower long term(not short term) inflation expectations putting downwardpressure on long term interest rates, relative to shortterm rates.

Government Finances can also affect the shape of theyield curve. Sustained budget deficits require increasedgovernment borrowing to fund them. Eventually, thisincreased supply in an increasingly global market wouldinduce investors to demand higher yields, resulting in aparallel shift of the curve.

Borrowers’ maturity preference changes can alter theslope of the yield curve. For example, the 2001 halt in USTreasury 30 year issuance created a shortage at the longend of the yield curve, pushing prices up, yields down,and flattening the curve. Similarly, a shift of corporateborrowing preferences between fixed and floating rateterms can alter the supply conditions at either end of theyield curve, changing its slope or curvature.

Demand Side FactorsGrowth and Inflation Expectations are key drivers atthe long end of the yield curve. Expectations of decliningeconomic conditions and correspondingly lower futureinterest rates can lead to a shift by investors into longermaturity, “safe haven” securities, pushing yields down,and leading to an inverted yield curve. Conversely,expectations of rapid economic expansion may lead to a steepening of the curve, as a result of the increaseddemand for capital, and the willingness to borrow forlonger maturities. A flat yield curve may signal uncertainty.Expectations of higher inflation, often linked to economicgrowth, will lead to an expected rise in nominal interestrates, and hence a steeper yield curve.

Worth noting is that the effect of demand and inflationaryshocks is not always straight forward. For example, achange in householder preference for current (over future)consumption has been consistently shown to induce alarge and persistent shift of the yield curve level. However,the yield curve effects of a sharp oil price shock, or atechnology driven supply shock are not as clear. This isbecause these type of shocks move output and inflationexpectations in opposite directions, and the yield curveeffect depends on whether the output or inflation responseis dominant.

Yield Curve Considerations

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Accretion – an increase of notional amount throughoutthe life of a structure.

American Option – an option that allows for exercise atany time during its life.

Amortisation – a decrease of notional amount throughoutthe life of a structure in a predetermined way.

Arrears – observation and fixing of the underlying rate atthe end of the coupon period as opposed to the start ofthe coupon period.

Barrier Options – options where the payoff depends on whetherthe underlying asset’s price reaches a certain level during acertain observation period.

Bearish – a view that an asset or underlying index willfall. In “rates” it means a rise in yields (a fall in price).

Bermudan Option – an option that allows for exercise atcertain discrete predetermined times during its life.

Bullet – an obligation that must be paid in a single lumpsum at the end of its term.

Bullish – a view that an asset or underlying index will rise.In “rates” it means a fall in yields (an increase in price).

Callable – the option but not the obligation for the issuerto redeem a security prior to its stated maturity, at apredetermined price.

Cap – an option that provides a payoff when a specifiedinterest rate is above a certain strike level. The interest ratecap can be thought of as a series of caplets which existfor each period the cap agreement is in existence.

Caplet – one component of an interest rate cap.

Clean Price – the price of a bond which does not includeaccrued interest.

Collar (or Corridor) – a combination of an interest ratecap and interest rate floor.

Collateralized Debt Obligation (CDO) – a way of re-packaging credit risk by dividing a pool of securities or financial assets into tranches. These tranches havedifferent risk and return profiles, essentially redistributingthe risk from the underlying portfolio.

Convexity – a measure of the curvature in the relationshipbetween price and yield. The greater the convexity, themore sensitive the duration is to changes in yield. Callablesecurities will exhibit negative convexity at certain price-yield combinations. Negative convexity means that asmarket yields decrease, duration decreases as well.

Correlation – a statistical measure describing the degreeof dependence between the fluctuations of two variables.

Credit Default Swap (CDS) – an agreement wherebyone party (the protection buyer) pays the other party (theprotection seller) a fixed periodic premium for a certaintenor. The protection seller makes no payments unless aspecified credit event occurs on a predefined reference entity.

Credit Event – an event which triggers payment in a Credit Default Swap. Common examples are bankruptcy,restructuring and failure to pay.

Credit Spread – the yield spread between risk freesecurities and others that are identical in all respectsexcept for credit quality.

Cross Currency Swap – the exchange of principal andinterest in one currency for the equivalent in anothercurrency at an exchange rate fixed at inception.

Currency Forward – A forward contract in the forexmarket that locks in the price at which an entity will buy or sell a currency on a future date.

Glossary

Convexity Bias is a factor which influences the long end of the yield curve. Convexity measures the curvature inthe relationship between bond prices and their yields.Bonds with high convexity perform better if rates change;if rates fall their price rises by more, if rates rise theirprice falls by less. The benefits of convexity cause moreconvex bonds to have higher prices and consequentlylower yields. Convexity increases strongly with maturityand is of great influence at the long end of the curve. Theconvexity bias therefore tends to lower yields at the longend of the curve.

Central Bank Reputation is also important. If the CentralBank has strong inflation fighting credentials, and if theyfollow a highly transparent monetary policy, then theyield curve may be flatter than it otherwise would. This isbecause concerns about future growth would outweighinflationary worries, and investors would require a smallerliquidity premium, because of the reduced uncertaintyabout future rate changes.

Foreign Central Bank purchases of government bondshave a significant effect on the shape of the yield curve.Countries with large foreign currency reserves resultingfrom current account surpluses are major buyers in thegovernment bond markets. A change in their preferenceover the maturity or currency of their purchases can havea major impact on the shape of the yield curve.

Regulatory Changes such as recent moves towardscloser asset/liability matching amongst pension funds,insurance companies, and other financial institutions have led to increased demand (and correspondingly lower yields) at the longer end of the yield curve.

Financial Innovation can also affect the shape of theyield curve. The emergence of structured notes has givenborrowers the flexibility of raising finance in maturities theywould not have otherwise considered. Through the processof “reverse inquiry” (whereby an issuance is driven by theinvestor’s, not the issuer’s, preference), investors have anincreasingly important influence on the supply and demanddynamics at a given point on the yield curve.

ConclusionWhilst numerous factors are clearly relevant in shapingthe term structure of interest rates, the graph belowsummarises the main determinants of the different partsof the curve.

Main Determinants of the Yield Curve

Yie

ld

Maturity

CentralBankMonetaryPolicy

Expectationsof FutureMonetaryPolicy

InflationsExpectationsand ConvexityBias

64 65

Notional – the cash amount over which the pay-off of aderivative or structured product is calculated.

Notional Effect – Apart from pure floating rate bonds,each bond displays the notional effect. This means thatthe mark-to-market price of a bond will be negativelyimpacted by an increase in interest rates, because anequivalent investment will pay a higher coupon in thissituation. The biggest notional effect is displayed in caseof fixed rate bonds, but also in case of structures withsome possibility of fixed coupons such as embeddedcaps and floors this effect will be displayed.

Out-of-the-money – an option is said to be out-of-the-money when its intrinsic value is zero, e.g. for a calloption when the spot price is lower than the strike price.

Par Value – the face value of a fixed-income asset.

Participation level (gearing) – the percentage of theprice change of the underlying index/asset that the buyerof a derivative contract is exposed to in relation to thatcontract’s notional amount.

Path Dependent – a feature for a derivative whereby the payoff depends on the whole path followed by theunderlying variable, not just its final value.

Quanto – a derivative in which the relevant performanceof the underlying asset or index is paid out in a foreigncurrency.

Sensitivity – the magnitude of a financial instrument’sreaction to changes in underlying factors, such as interestrates.

Spot Price – the current market price for an asset orindex.

Straddle – an option strategy primarily used to profitfrom an increase in volatility. It involves buying a call anda put with the same strike price and expiration date. Aloss will occur if the spot price is close to the strike priceat expiration of the options.

Strike Price – the predetermined price for which theunderlying asset/index may be purchased or sold by the investor upon exercise of the derivative contract.

Structured Note – a debt obligation that contains aderivative component to achieve a specific risk/rewardprofile.

Swap – an agreement between two parties to exchangedefined cash flows over a period of time.

Swaption – the option to enter into a swap. In exchangefor an option premium, the buyer gains the right but notthe obligation to enter into a specified swap agreementwith the counterparty on a specified future date.

Underlying Asset – the asset or index upon which thevalue and pay-off of a derivative contract is based.

Vanilla – the most basic version of a derivative contract.

Vega – a measure of an option’s sensitivity to volatility. Itshows the change in the option’s value resulting from asmall change in volatility of the underlying index.

Volatility – the annualised standard deviation of an asset’sreturn. It is a measure of the variability of the asset price.

Yield – the annual rate of return for a security.

Yield curve – the relationship between yields and maturitiesfor a given security (also known as the Term Structure).

Delta – a measure of the sensitivity of a derivative tochanges in its underlying asset or index.

Derivative – a financial contract whose price and cashflows are dependent upon one or more underlyingassets.

Digital (or Binary) – a derivative product for which the payout is a fixed cash amount (“high payout”) if theinvestor’s view proves to be correct, and zero (or “lowpayout”) otherwise.

Dirty Price – the price of a bond which includes theaccrued interest.

(Modified) Duration – the measure of the pricesensitivity of a fixed-income security to an infinitesimalchange in yield. The greater the duration, the greater thesensitivity to interest rate movements.

European Option – an option that can only be exercisedat the end of its life.

Exotic – structured products which are more complexthan the derivatives usually traded on an exchange. Asopposed to vanilla products, they are generally tradedover the counter.

First-To-Default Basket (FTD) – provides multiple nameexposure in a CLN. An investor in a CLN with a FTDfeature runs full principal risk in case of a credit eventon any of the names in the underlying basket.

Floor – an option that provides a payoff when a specifiedinterest rate is below a certain strike level.

Floorlet – one component of a floor. The interest ratefloor can be thought of as a series of floorlets which existfor each period the floor agreement is in existence.

Forward Curve – a graph of forward rates for differentmaturities.

Forward Rate – the interest rate for a future period oftime implied by the rates prevailing in the market today.

Hedge Fund – a discretionarily managed portfolio ofinvestments that uses strategies such as leverage, long,short and derivative positions with the goal of generatingabove market returns at an acceptable level of risk.

Historical Volatility – the volatility of a financialinstrument actually realised over a given period in the past.

Hybrid – a derivative product that depends on theperformance of two or more underlying assets or indices.

Implied Volatility – the future volatility of an instrument’sprice estimated from derivatives currently traded in themarket.

In-the-money – an option is said to be in-the-moneywhen its intrinsic value is positive, e.g. for a call optionwhen the spot price is higher than the strike price.

Internal Rate of Return (IRR) – the discount rate thatmakes the net present value of future cash flows equalto zero.

Knock-in Option – a type of barrier option which onlycomes into existence if a certain barrier is hit.

Knock-out Option – a type of barrier option whichceases to exist if a certain barrier is hit.

Leverage – the use of derivatives or borrowed capital toincrease notional exposure to an investment.

Lifetime Cap – the maximum cumulative coupon amountthat an investor in for instance a Target Redemption Notecan earn. When this level is reached, the product isgenerally automatically redeemed.

Mark-to-market (MtM) – the act of recording the priceor value of a security to reflect its current market valuerather than its book value.

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