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1/14

Synthetic Credit Options

Trading Credit Risk and Credit Volatility via Options

March 2012

Abel ElizaldeAC

Credit Derivatives and Quantitative Credit Research

J.P. Morgan Securities Ltd

[email protected]

+44(0) 20 7742 7829

This presentation was prepared exclusively for instructional purposes only, it is for your information only. Itis not intended as investment research. Please refer to disclaimers at back of presentation.

Synthetic Credit Options

Trading Credit Risk and Credit Volatility via Options

Payer and receiver options

Definition, payoffs & mechanics

O tion cost and breakeven s reads

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Pricing

Expressing spread and volatility views using credit options

Volatility

Implied vs. realised, term structure & skew

Option to buy/sell protection at a future date at an agreed spread

Options on CDS Indices (iTraxx Europe, Crossover, Financials, CDX IG) and Single Name

CDS (less liquid).

Main features:

European style: only exercisable at expiry.

Options on Credit Derivatives

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5 year underlying CDS.

Most liquidity in volatile underlyings, e.g. iTraxx Crossover index

Liquid maturities: 3, 6, 9 months

Strike is quoted in a full running format.

Well focus on the mechanics & pricing of options on single name CDS. Options on CDSindices work in a similar way except for a few differences that we will highlight.

Receiver

Right to sell protection, i.e. put option on CDS spread

Payer:

Right to buy protection, i.e. call option on CDS spread

Receiver & Payer Options

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Alternatives:

Buy receiver option: buy the right to sell protection

Sell receiver option: sell the right to sell protection

Buy payer option: buy the right to buy protection

Sell payer option: sell the right to buy protection


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3/14

Payer Options Payoff

Buy Payer Option

300

400

500

5,0

5,5

6,0

Payoff = (Spread Strike)*DVO1 Premium

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-100

0

100

0 25 50 75 100 125 150 175 200

3,0

3,5

4,0

,

Payof f (LHS) DVO1 (RHS)

ecreases

with spread

Source: J.P. Morgan.

Receiver & Payer Exposure

Buy payer Sell Payer Buy Receiver Sell Receiver

Buy Sell Buy Sell

Right to Buy protection Buy protection Sell protection Sell protection

Spread exposure Short Long Long Short

Spread Vol. Expoure Long Short Long Short

Credit (risk) exposure

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Risk factors

Spreads

Spread volatility

Interest rates

Default of the underlying

What happens to the option contract if the underlying defaults before the optionexpiry?


The option contract can:

Knock-Out

Option is terminated at the time of default: no payments, no exercise.

No Knock-Out

Knock-Out and No Knock-Out

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The option buyer has the right to exercise the option. The option gives theright to buy or sell protection in a credit which has defaulted. Buyers of payeroptions will exercise, buyers of receivers will not

When is the option exercised? Two possible cases:

Now (i.e. at the time of default): Option acceleration

At option expiry: No acceleration

What is the impact of knock-out in an option premium?

Payer option:

More expensive without Knock-Out

It would always be profitable to exercise a payer option on a defaulted name

(You would be buying protection, at a fixed spread, on a defaulted name;

Upon Default

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receiving 1 Recovery)

Receiver option:

No price impact

Upon default, you would never exercise a receiver option

(You do not want to sell protection, at a fixed spread, on a defaulted name)


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Assume you buy a payer option with notional 1 and expiry T

Knock-out option

Scenario 1: No default .

Scenario 2: Default before expiry ..

No Knock-out option (no acceleration)

Payer options: More expensive without Knock-Out

]0,1)max[(TT

DVOKS

0

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Scenario 1: No default .

Scenario 2: Default before expiry ..

In the No Knock-Out case the payoff is equal or better; thus, its price must be higher

Repeat this exercise for a receiver option and show that, in that case, the payoffs of aKnock-Out and No Knock-Out options are the same no matter whether there is a defaultor not.

]0,1)max[( TT DVOKS

01]0,1max[ >= RR

Consider a single name CDS option, What will be more expensive?

Payer option, No knock-out, with acceleration.

Payer option, No knock-out, without acceleration.

Repeat the exercise of the previous slide considering the two alternatives above.

Payer options with No Knock-Out

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Single name options are generally traded with Knock-Out

Index options are generally traded with No Knock-Out (and No Acceleration)

What happens in an index option if there is a default before the expiry?

Knock-Out and No Knock-Out: Single name vs. Index options

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Will the buyer of payer index options always exercise if there has been one default?

Expressing a bullish view on spreads

Sellindex

protection

Simplest strategy to take a view on

spread tightening

Linear return profile if spreads widen ortighten

Unlimited downside risk if spreads widen20bp 50bp 80bp

er

Limit downside risk by buying a receiveroption

Decreasing priceIncreasing spreads

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BuyRecei

Full upside in spread tightening (minus

premium)20bp 50bp 80bp

SellPay

er

Bullish view if believe spreads will

tighten but not past x

Strategy outperforms selling indexprotection for levels above x

20bp 50bp 80bpX





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Expressing a bearish view on spreads

Bu

yindex

protection

r

Simplest strategy to take a view onspread widening

Linear return profile if spreads widen or

tighten

Downside risk capped as spreads cannotbe negative

20bp 50bp 80bp

Limit downside risk by buying a payeroption


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BuyPaye

SellReceiver

Full upside in spread widening (minus

premium)

Maximum loss limited to premium paid

for option

20bp 50bp 80bp

Bearish view if believe spreads will widenbut not past x

Strategy outperforms buying index

protection for levels below x20bp 50bp 80bpX




Assuming there is no default, the breakeven spread of an option is the spread for the

underlying at the option expiry which generates a total PnL equal to zero.

For a payer option:

Breakeven Spreads

KCost

S

CostDVOKSCDS

TP

TTTP

+=

=

*

,

*01]0),max[(

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For a receiver option:

We use the forward DVO1 to compute the expected breakeven spread

DVOCDSTT,

1

CDS

CDS

TT

TR

TTTR

DVO

CostKS

CostDVOSK

,

*

,

*

1

01]0),max[(

=

=

We are concerned about a spread widening and want to buy protection using options(9-Mar-09)

We choose to buy an OTM (1300bp Strike) Payer on 5y iTraxx Crossover on $10,000,000notional

Cost (Premium) of the option is quoted at 392c in the market, for a Jun 20th 2009 expiry

Current spread on iTraxx Crossover is 1150bp

A Simple Example Entering the Options Contract

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This means we are buying the option (right) to buy iTraxx Crossover protection (short risk)at 1300bp on $10,000,000 notional on Jun 20th

Costs

We have to pay 392c on $10,000,000 notional to

enter the contract

Cost = (392/10000) * $10,000,000 = $392,000

Option P+L at Expiry

1000bp 1300bp 1600bp

Buy Payer

iTraxx CrossoverSpreads


Breakevens

We will be buying protection at 1300bp, so at first thought if spreads are above1300bp at expiry well make money

But, as we saw, the cost of the option was 392c

So, we need the index to widen more than 1300bp to make-up for the cost

A Simple Example - Breakevens

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We nee to in t e rea even sprea at expiry

Option P+L at Expiry

1000bp 1300bp 1600bp

Buy Payer

iTraxx CrossoverSpreads

Breakeven Spread



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7/14

Modelling Single-Name and Multi-Name Credit Derivatives D. OKane. 2008.

Chp. 9: Forwards, Swaptions and CMDS, and references therein.

Here, we outline the pricing of options on single name CDS. However, most of theliquidity is around options on CDS indices. For details on the pricing of CDS index options

see:

References on CDS Option pricing

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Chp. 11: Options on CDS Portfolio Indices, and references therein.

Options on CDS indices do not knock-out and do not accelerate.

Compared to single name CDS options, the pricing of options on CDS indices should

take into account the fact that the index does not disappear even if somecredits default.

Consider the case of a knock-out single name CDS option

Payer payoff at maturity:

Receiver payoff at maturity:

Pricing: Option Payoffs

]0,1)max[( TT DVOKSPO =

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Where is the CDS spread at option expiry T, is the option strike, and

is the CDS DVO1 at expiry T

K

TDVO1

TS

]0,1)max[( TT DVOSKRO =

If default happens before option expiry, will be zero

Assuming the CDS spread follows a Geometric Brownian Motion, one can apply the

Black-Scholes machinery for option pricing

Modified Black-Scholes

TDVO1

No Exam

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TT DVOSKRO 1]0),max[( =

TTDVOKSPO 1]0),max[( =

Equity call payoff at expiry

where Tis the option maturity, S is the stock price, and C is the call option price.

(equities, i.e. the underlying, do not have a maturity; however, CDS do!)

Black-Scholes for Equity Options

]0),max[( KSC TT =

No Exam

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Assume risk neutrality and equity price follows a Geometric Brownian Motion

where is the interest rate, the volatility and a Browniam MotiontWr

tttt dWSdtrSdS +=


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Call price

(Today 0, expiry T)

Black-Scholes for Equity Options

dNeKdNSC

rT

rT

=

2100 )()(

No Exam

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TddT

TKSEd

eSSE

T

rT

T

T

=

+=

=

=

12

2

1

0

21

;2/)/][ln(

][

Using a similar derivation than for equity options

Payer price (Today 0, option expiry T, underlying CDS maturity TCDS)

Black-Scholes for CDS Options

DVOdNKdNFP CDSCDS TTTT = ,21,0 1)]()([

No Exam

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FT,TCDS and DVO1T,TCDS are the forward spread and duration of a CDS contract starting at T

and maturing at TCDS.

We can compute them using an arbitrage argument and the spread and durations of CDS

contracts which start today and mature at Tand TCDS

TddT

TKFd CDS

TT

=+

=12

,

1;

2/)/ln(

Payer and receiver option prices (with knock-out)

Black-Scholes for CDS Options

CDSCDS TTTT

DVOdNFdNKR

DVOdNKdNFP ,21,0

1

1)]()([

=

=

No Exam

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What if the option does not knock-out?

Receiver does not change

Payer should be more expensive

What is the value added of the No Knock-Out in a payer option?

CDSCDS ,,

As we argued before, the holder of a receiver option will never exercise it if the CDS has

defaulted since it would result in a loss.

For a payer option:

Value of No-Knock Out Payer = Value of Knock-Out Payer + Value of No-Knock OutFeature

Payer & No Knock-Out

No Exam

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If there is no default, the No-Knock-Out feature does not kick in

In case of default, the buyer of the payer receives (1 Recovery)

At the time of default, if the option accelerates

At option expiry, if the option does not accelerate


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10/14


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12/14

N E N E


13/14

No Exam

Selling Credit Volatility Three Variations

Selling credit volatility is most successful after a sell-off dueto the high spread levels and high implied volatilitiespushing up the price of straddles; the two most successful

periods for this strategy has been the months following

Lehmans collapse in 2008 and 2H11.

Jumps in realised volatility normally c ause a short term lossin the VICI index but this is quickly made bac k from sellingvolatility at the new higher levels of implied volatility.

Selling Credit Volatility P&L from selling short dated iTraxxM ain vol since 2006

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48Source: J.P. Morgan.

Crossover, Senior Financials and CD X IG.

Source: J.P . Morgan

Further information on theP&L from selling creditvolatility and the VICI indices

is available in:Credit Volatility Indices:Adding Alpha With CreditVolatilityD. White, March 2011

PnL of Selling Implied Vol (Sell Straddles, Delta-hedged)

No Exam

iTraxx Main iTraxx Main vs. Crossover

15%

20%

25%

30%

35%

40%Crossover 1m

Main 1m

4%

6%

8%

10%

12%

14% Main 1m

Main 3mMain 6m

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49Source: J.P. Morgan.

-5%

0%

5%

10%

Mar-07 Mar-08 Mar-09 Mar-10 Mar-11-4%

-2%

0%

2%

Mar-07 Mar-08 Mar-09 Mar-10 Mar-11

Greeks

Date:

6-Apr-10

Expiry:

16-Jun-10

Index:

Crossover 5y

No Exam

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Delta: Index position which generates a similar spread exposure than the option (in MtM terms) for small spreadmovements.

Gamma: As spreads move, the delta of an option changes. As a consequence, an initially delta-hedged option willnot be perfectly delta-hedged as spreads move. Gamma indicates the change in an options delta as spreadsmove.

Theta: If you buy an option, how much do you lose (in cents) in one day if everything else (spreads, volatility,rates, defaults) remains constant.

Vega: If you buy an option, how much do you make (in cents) if volatility increases 1% if everything else (spreads,time, rates, defaults) remains constant.


Volatility Term Structure

Same strike, differentexpiry: Different

Volatility

No Exam

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Why?


No Exam


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Volatility Skew

Same expiry, differentstrikes: different

volatility

No Exam

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Why?


Disclaimer

JPMorgan is the marketing name used on research issued by J.P. Morgan Securities Inc. and/or its affiliates worldwide. J.P. Morgan Securities Inc. (JPMSI) is a

member of NYSE, NASD and SIPC. This presentation has been prepared exclusively for the use of attendees at Imperial College Structured Credit and Equity

Products" Course and is for information purposes only. Additional information available upon request. Information has been obtained from sources believed to

be reliable but JPMorgan Chase & Co. or its affiliates and/or subsidiaries (collectively JPMorgan) does not warrant its completeness or accuracy. Opinions and

estimates constitute our judgment as of the date of this material and are subject to change without notice. Past performance is not indicative of future

results. This material is not intended as an offer or solicitation for the purchase or sale of any financial instrument. Securities, financial instruments or

strategies mentioned herein may not be suitable for all investors. The opinions and recommendations herein do not take into account individual client

circumstances, objectives, or needs and are not intended as recommendations of particular securities, financial instruments or strategies to particular clients.

The recipient of this report must make its own independent decisions regarding any securities or financial instruments mentioned herein. JPMorgan may act asmarket maker or trade on a principal basis, or have undertaken or may undertake an own account transaction in the financial instruments or related

instruments of any issuer discussed herein and may act as underwriter, placement agent, advisor or lender to such issuer. JPMorgan and/or its employees may

hold a position in any securities or financial instruments mentioned herein.

Copyright 2012 JPMorgan Chase & Co.All rights reserved.

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