pratical fixed income_eisti 2015
TRANSCRIPT
Practical Fixed Income
Practical Nominal Fixed Income
I. Conventions and Curves theories
II. Bonds, Discounting Methods and Forward
III. Durations and Convexity Risk
I. Conventions and Curves theories
Base Exact/360 ( “Money Market Basis” )
Numerator : Period defined with exact number of days ( varies
between 28 to 31)
numerator = exact numbers of days
Denominator :360
Base 30/360 ( “Bond Market Basis” )
Numerator : Period defined with as months of 30 days max (varies
between 28 to 30)
formula : (J2-J1) + (30 x (M2-M1) ) + (360 x ( A2-A1))
Denominator :360
Conventions
Base Exact/365 ( ZC base)
Numerator : Period defined as exact number of days ( varies between
28 to 31)
formula : numerator = exact numbers of days
Denominator :365
Base Exact/Exact
Numerator : Period defined as exact number of days ( varies between
28 to 31)
formula : numerator = exact numbers of days
Denominator :365 or 366 if bissextile
Conventions
Impact of the different basis
Example : From 09 Jan 2014 to 30 Jun 2014
a) Exact/360 : 0.4777
b) 30/360 : 0.475
c) Exact/365 : 0.47123
d) Exact/Exact : 0.47123
Conventions
Payment Convention
If the payment date comes on non-working day, few rules
apply
Convention “Previous Business Day” :
o Payment on the previous working day
Convention “Following Business Day” :
o Payment on the following working day
Convention “Modified Business Day” :
o Payment on the following working day except if it changes the
payment months
Conventions
Standard European Curves EONIA (Euro Overnight Indexed Rate Average)
– Daily average rates weighted by interbank deposits in the euro
zone
– Capitalized EONIA is used in the OIS Swaps for example
– Published by the European Bank Federation
EURIBOR (Euro Interbank Offered Rate)
– Average rate at which a sample of European banks are lending
money
– Fixing every working days at 11am (French time), maturity from 1
to 12 months
– Published by the European Bank Federation
International Standard Curves
– Each important financial place has an interbank average rate that
are used as a reference for Swaps in a given currency ( ex: SONIA,
LIBOR…)
Definition of the yield curve
– The yield curve is the “term structure” of interest rates
Explanations :
– For a given maturity and a given credit risk, there is a given
interest rate.
– There are many yield curves according to a country, a currency
and of the credit risk
Yield curve
Bonds
Market curves
Directly defined by the market quotes of financial instruments
(swaps, bonds).
Ex: Government Bonds
Implied curves
Indirectly defined by the market quotes of financial instruments
(swaps, bonds).
Ex: Forward, zero-coupon bond
Drafting the yield curve
Standard forms of the yield curvesrate
maturity maturity
maturitymaturity
raterate
rate
Yield curve theory
The theory of anticipation (increasing curve)
The long term rates are the reflection of the anticipation of the
short term rates in the future => anticipated short term rates are
higher than the actual short term rates.
The theory of the preference for liquidity (increasing
curve)
The financial instruments with longer maturity are less liquid and
more risky => the long term rates must be higher
Yield curve theory
The theory of the segmentation (random curve)
Each segment of the yield curve (0-5 years, 5-10 years,> 10
years..) represents segments of the market with their own offer
and demand => independency of the segments
The theory of the preferred segment (random curve)
The actors on the market have a preference for certain segments
on the yield curve. Here the actors can intervene on many
segment of the curve ( difference between the theory of
segmentation)
Yield curve distortions
Parallel distortions
The entire curve is distorted in a uniform way
Ex:
The yield curve increase by 1% on all the maturity
rate
maturity
C0
C1
+1%
Yield curve distortions
Non Parallel distortions
The entire curve is distorted not in a uniform way
1) Steepening
Various possibilities :
rate
maturity
C1
C0
C1’
Higher long term rates
Lower short term rates
Yield curve distortions
2) Flattening
Various possibilities :
rate
maturity
C1
C0
C1’
Higher short term rates
Lower long term rates
Yield curve distortions
3) Modification of the curve
rate
maturity
C0
C1
Higher MT rates Lower ST and LT rates
Standard European Curves
3) Modification of the curve
rate
maturity
C0
C1
Higher MT rates Lower ST and LT rates
II. Bonds, Discounting Methods and
Forward
Bloomberg Print Screen:
Bonds
Actuarial Yield :
Bonds
– P is the bond price– C is the periodic coupon payment– N is the number of years to maturity– M is the (face value) payment at maturity (100)– y is the yield to maturity or actuarial yield
NN32 1
M
1
C...
1
C
1
C
1
CP
yyyyy
Actuarial Yield :
Bonds
– Bond price is 99.5– Maturity is 5y– Coupon is 2.9%
What ‘s the value of the yield to maturity ???
55432 1
100
1
2.9
1
2.9
1
2.9
1
2.9
1
2.999.5
yyyyyy
Spot rates :
Bonds
– P is the bond price– C is the periodic coupon payment– N is the number of years to maturity– M is the (face value) payment at maturity (100)– spot rate rn is the discount rate for a cash flow in year n that
can be locked in today
P C
1 r1
C
1 r2 2 C
1 r3 3 ... C
1 rN N M
1 rN N
Bonds
Advantages of the yield to maturity:
• Allows investors to compare different bonds with each
other
• Good sensitivity of the bond proxy
Disadvantages of the yield to maturity measure:
• Considers the curve flat
• Movement only in parallel shift
Bonds
Maturity from 1day to 12 months:
• We use the money market rates ( Euribor) in order
to get the zc rates.
• No calculation needed as they are all ready zc
rates.
• It is expressed in basis ( exact/360) => we convert
it into exact/365 ( base for zc )
• For one day we use the EONIA rate ( money rate)
that we convert into zc rate base :
Discounting ZC method
1))360
(1(365
nMzc
nTT
Maturity over 1y :
• We use the “bootstrapping” with the swap rate that is
quoted in the market to get the imply zc rate
Discounting ZC method
100
100
100
)1(
1)1(
1)1(
1
100
100
100
33
22
11
333
22
1
zc
zc
zc
TwTwTw
TwTw
Tw
CBA
CAB 1
Discounting ZC method
Maturity ZC Rates 0.00 0.100%0.02 0.132%0.08 0.187%0.25 0.260%0.50 0.355%0.75 0.298%1.00 0.531%
2 0.531%3 0.727%4 0.978%5 1.230%6 1.464%7 1.676%8 1.868%9 2.040%
10 2.194%11 2.328%12 2.442%13 2.540%14 2.620%15 2.684%16 2.735%17 2.773%18 2.799%19 2.817%20 2.830%21 2.842%22 2.855%23 2.851%24 2.852%25 2.845%26 2.841%27 2.837%28 2.830%29 2.823%30 2.816%
tickerMarket Rates
EONIA Curncy 0.10%EE0001W Index 0.13%EE0001M Index 0.18%EE0003M Index 0.26%EE0006M Index 0.35%EE0009M Index 0.29%EE0012M Index 0.52%EUSA2 Curncy 0.53%EUSA3 Curncy 0.73%EUSA4 Curncy 0.97%EUSA5 Curncy 1.22%EUSA6 Curncy 1.44%EUSA7 Curncy 1.65%EUSA8 Curncy 1.83%EUSA9 Curncy 1.99%EUSA10 Curncy 2.13%EUSA11 Curncy 2.25%EUSA12 Curncy 2.35%EUSA13 Curncy 2.44%EUSA14 Curncy 2.51%EUSA15 Curncy 2.56%EUSA16 Curncy 2.61%EUSA17 Curncy 2.64%EUSA18 Curncy 2.67%EUSA19 Curncy 2.69%EUSA20 Curncy 2.70%EUSA21 Curncy 2.71%EUSA22 Curncy 2.73%EUSA23 Curncy 2.73%EUSA24 Curncy 2.73%EUSA25 Curncy 2.73%EUSA26 Curncy 2.73%EUSA27 Curncy 2.73%EUSA28 Curncy 2.73%EUSA29 Curncy 2.73%EUSA30 Curncy 2.72%
Forwards and Futures Definition
– A forward is a OTC contract that allows to fix spot the rates of a
loan in a given period and a defined amount.
– Forward aims at a future loan/ placement
– The operation will actually take place with a redemption of the
notional at the determined rate and for a given maturity (not the
case for a future nor a FRA)
– The forward rate curve is calculated thanks to the spot rate curve :
in is based on the market efficiency principal.
Conclusion : The present value of a spot placement at the 1 year
market rate followed by a placement for a year in a year
Must be equal to
The present value of a spot placement at the 2 year market rate
Forward:
• As there is no arbitrage, we have the following
formula :
• : investment spot rate for N years
• : Forward rate for 1year in 1year
Forwards and Futures
20,2
11,1
10,1 )T(1)F(1)T(1
N0,T
1,1F
FRA: Forward Rate Agreement
• Cash settled contract on a short-term loan
• OTC
• The underlying loan is usually for 3 or 6 months, and quotes
generally for 1×4, 1×7, 3×6, 3×9, 6×9 and 6×12
• Buyer of means “payer of fixed rate in x
Months for y Months
• The variable rate is determined at maturity and the
counterparties exchange just the differential with the
fixed rate
Forwards and Futures
yx,FRA
FRA: Forward Rate Agreement
Value of the FRA formula :
Forwards and Futures
)1),((
),((
1 ),,(F
))
360T1(
360)T(T
(n Value
ref
Fixref
TtDF
TtDFTTtRA
days
days
n : notional amount of the loan
days : number of days the loan
FRA
EURIBOR
:T
:T
ref
Fix
Futures : Short term ( cash settlement)
• Those futures represent fictive bonds defined with a
nominal, a maturity and a coupon
• It is quoted in price by the yield rate
Forwards and Futures
Yield100Price Future
Futures : Euribor3m
• Maturity 90 days
• Notional 1m
• K : numbers of contracts
• : Price of the Future at time t
Forwards and Futures
)(1000000&
))360
90((1(Price Future Actual
0
3
FFKLP
TN
f
ME
tF
Futures : Bund, Bobble, Schatz…
• Those futures represent fictive bonds defined with a
nominal, a maturity and a coupon
• At expiry date, several bonds that exist in the fixed
income market will be deliver at a price that will reply
the future properties
Forwards and Futures
Futures : Bund Future :
• Notional short-, medium- or long-term debt instruments issued by the Federal Republic of Germany, the Republic of Italy, the Republic of France or the Swiss Confederation with remaining terms and a coupon
Forwards and Futures
FactorConversion
CCfundingCTD_BondCTD_Bond
Future
PricePrice
Futures : Bund Future :
• The conversion Factor is specific to each cheapest and
is calculate at the issue of the new future ( same YTM
between the future and the cheapest)
• quick approximation :
Forwards and Futures
Future
CTD_Bond
Price
)(PV discountedYTMFactorConversion Future
Futures : Bund Future :
• Issue 07/06/2014 : Bund Future =143
• CTD Price : YTM = 1.545
Forwards and Futures
Future
CTD_Bond
Price
)(PV discountedYTMFactorConversion Future
Futures : Bund Future :
• : Price at t0
• : Price at tf ( closing of the trade)
• K : Numbers of Contracts
Forwards and Futures
)(100000& 0FFkLP f
0F
fF
Futures : Bund Future :
Forwards and Futures
III. Durations and Convexity Risk
Durations and Convexity Risk
Taylor-Young Formula
• Formula :
)(xf !
h...)(xf
!2
h)(xfh )f(x h) f(x 0
nn
0''
2
0'
00 n
Durations and Convexity Risk
Duration : “Macauly Duration”
• It measures of average maturity of the bond’s
expected cash flows
• Formula :
T
t
ttD1 PV(Bond)
)C(PV
NN
NN
yyy
yN
yyD
)1(
C...
)1(C
)1(C
)1(C
...)1(
C2
)1(C
1
22
11
22
11
Durations and Convexity Risk
Duration : “Macauly Duration”
• Duration is shorter than maturity for all bonds except zero coupon bonds
• Duration of a zero-coupon bond is equal to its maturity
Durations and Convexity Risk
Modified duration :
• Formula :
• Direct measure of price sensitivity to interest rate changes
y
DurationDm
1
Durations and Convexity Risk
Modified duration :
• Formula :
Dm measures the sensitivity of the % change in bond price to changes in yield
m
m
N
tt
tN
tt
t
Dy
P
P
PDy
Ct
yy
P
y
CP
1
)1(1
1
)1( 11
Durations and Convexity Risk
Convexity Risk:
• Formula :
y
P
P
tty
CF
yy
P N
tt
t
2
2
1
222
2
1Convexity
)()1()1(
1
Durations and Convexity Risk
Convexity Risk:
Durations and Convexity Risk
Convexity Risk:
• Measures how much a bond’s price-yield curve deviates from a straight line
• Second derivative of price with respect to yield divided by bond price
• improve the duration approximation for bond price changes
Durations and Convexity Risk
Example : DBR 4.75% 04/07/28
Futures : Bund Future :
Forwards and Futures
Durations and Convexity Risk
Example : ( Price : 131.64; yield : 2.171)
DBR 4.75% 04/07/28 • Duration : 11.053
• Modify Duration : 10.817
• Convexity : 1.487
Bund ( Price : 142.95)
• Duration : 8.382
• Modify Duration : 8.254
• Convexity : 0.799
Durations and Convexity Risk
Future Hedge Ratio : Bund
• In order to cover our rate risk, we use the Modify Duration of our bond vs the Modify Duration of the CTD bond
• Ratio :
Where MD is the modify duration
FactorConversionMD
MD
CTDice
eBondMarketValuatio
CTD
BOND
1000)(Pr
R
Durations and Convexity Risk
Example :
• Hedge Ratio :
For 25m DBR 4.75% 04/07/28 , we have 302 bund contracts
695531.0254.8
817.10
100054.99
64.131R
atio
Fixed Income Product : Swap
Swap :
• A swap is an over-the-counter (“OTC”) derivative transaction where the counterparties agree to exchange cash flows linked to specific market rates for a period of time.
• One set of cash flows will typically be known – usually expressed as a fixed rate of interest. The other set of cash flows will be unknown – example : Euribor6m
• the present value of both sets of cash flows is the same at inception.
Periodic exchange of cash flows for life of transaction
Fixed payments
LIBOR payments - unknown
Fixed Income Product : Asset Swap Par/Par
Asset Swap Par / Par :
• An asset swap is a derivative transaction that results in a change in the form of future cash flows generated by an asset
• In the bond markets, asset swaps typically take fixed cashflows on a bond and exchange them for Euribor + spread (i.e. floatingrate payments)
• At inception the investor and the counterparty exchange the following flows :
Fixed Income Product : Asset Swap Par/Par
Asset Swap Par / Par :
Fixed Income Product : Z-Spread
Z- Spread:
• The Z-spread is a purely theoretical concept designed toallow a bond yield to be compared to a swap rate as fairly aspossible
• The Z-spread is defined as the size of the shift in the zerocoupon swap curve such that the present value of a bond’scash flows is equal to the bond’s dirty price
Pure RV indicator
Practical Inflation Fixed Income
I. Inflation Market
II. Inflation Products and Inflation Curve
III. RV Strategy
I. Inflation Market
Inflation Market
Inflation
Markets
Clients
Regions Instruments
Inflation Market
HEDGING
* Pension Funds
* Insurance Companies
* Retail
* ALM / Treasury
* Corporates
* Utilities
* Infrastructure Projects
* Real Estate Companies
Clients
BENCHMARKING
* Inflation Funds
* Mutual Funds
RELATIVE VALUE
* Hedge Funds *
* ALM / Treasury *
* Pension Funds
* Insurance Companies
* Retail
* Inflation Funds *
* Asset Swap Investors
ISSUERS
* States
* Agencies
* Corporates
*Receiver *Payer
Inflation Market
Inflation Payers :
Payers of inflation are entities that receive inflation cashflows in their
natural line of business as their income is linked to inflation. Therefore
they’ll sell it in the inflation market. ( sovereigns will issue inflation
bonds for example)
Inflation Receivers :
Inflation receivers are entities that pays inflation cashflows in their
natural line of business as their liabilities are linked to inflation.
Therefore they’ll buy it in the inflation market. ( PF will be short on their
long term inflation liabilities if they don’t buy inflation securities to
counterbalance their shortfall risk)
Shortfall risk: risk that their assets drop below their liabilities
Inflation Market
EUROPE
The most sophisticated derivatives market
Big cash market, international interest
More buyers than sellers
Domestic indices
Sale/leaseback Retail demand: more to
structured products
A lot of ASW investors
USA
Biggest cash market
ASW investors
Limited options appetite
Lack of contractual buyer or seller of
inflation
UK
The first market to issue a linker
The longest linkers
Balanced buyers and sellers
Huge corporate issuance
Plenty of contractual buyer and seller of
inflation
LPI vs RPI
Retail demand: linker format
ASW investors
JAPAN &
AUSTRALIA & EMJapan- mainly on
bonds
Deflation is an issue
Australia- similar to the UK
EM- LatAm is growing fast
On shore/off shore
Regions
Fig. 1:Weights in the US CPI
Source: Deutsche Bank
Fig. 2:Weights in the UK RPI
Source: Deutsche BankFood and cateringAlcohol and tobaccoHousing andhousehold expenditure Personal expenditure Travel and leisure
Food and beveragesHousing Apparel Transportation Medical Care Recreation Education and Communication Other
46 165
2577 88
%
821742
408
Fig. 3:Weights in the EUR
Source: Deutsche Bank Food & beverages
Alcohol & tobaccoClothing & footwearHousing & household services Furniture & household goods HealthTransport Communication Recreation & culture Education Restaurants & hotelsOther goods & services
99 1
4
7 10%
316
167 4
Inflation Market
May 201
3
CPI
Published every month
Delay between the months and the publication of the figure cannot be used directly for indexation
An indexation lag is then needed (for example 3 months for OATeis)
DRI
In order to calculate accrued interest on inflation, one has developed a daily reference index (DRI)
Daily figure calculated as a linear interpolation between the published CPI with a 2 and 3-month lag
DRI (01 May 2013) = CPI (Feb 2013) = 115.55 DRI (01 June 2013) = CPI (March 2013) = 116.94
DRI (10 May 2013) = linear interpolation between the 2 figures
Inflation Market
May 201
3
CPI and DRI : calculation
CPI Feb
115.55 CPI Mar
116.94
01-Feb 01-Mar 01- Apr 01-May 01- Jun
5 10 15 20 25
115.55
116.94
115.78
116.01
116.48 116.25
116.71
Publication
20 Mar
Publication
20 Apr
Inflation Products
Inflation Market
Instruments
REAL YIELD
Inflation-linked bonds
Nominal bonds vs inflation swaps
BREAKEVENInflation swaps
Inflation-linked bonds vs nominal
swaps
VOLATILITY
Caps & Floors
Swaptions
ASW options
Bond options
Real rate vol
ASW
Bond asset swaps
Cash breakeven vs swaps breakeven
Nominal yield Yield of a conventional government bond (Treasury, Gilt, OAT...)Real yield Yield of an inflation-linked government bond (TIPS, Indexed Gilt, OATi, OATei...)Breakeven inflation (BEI) Inflation implied by the level of real and nominal yields
The Fisher Equation: (1+ Nominal Yield) = (1+ Real Yield)* (1+ Breakeven Inflation)
Real Yield ~ Nominal Yield – Breakeven Inflation
72
-1.00%
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
0 5 10 15 20 25 30
Breakeven inflation
Real yield
Nominal yield
Inflation Market
73
Yield oat oct23 = be oati23 + Real Yield oati23
Inflation Market
Inflation Expectation + (Liquidity Premium + Risk Premium)
Break-Even Inflation
Inflation Market
• Break-Even mainly indicates how much inflation the
market expects.
• Liquidity Premium : as inflation bonds are less liquid
than nominal bonds the market price a liquidity
Premium
• Risk Premium : If inflation uncertainty is high than
premium investor demand for holding such bond is
high as they are risk averse
Real Yield :
– P is the bond price– C is the periodic coupon payment– N is the number of years to maturity– M is the (face value) payment at maturity (100)– y is the yield to maturity or actuarial yield
NN32 1
M
1
C...
1
C
1
C
1
CP
rrrrr yyyyy
Inflation bond – Structure
Inflation Market
Inflation Market Inflation bond – Structure
The Fisher Equation: (1+ Nominal Yield) = (1+ Real Yield)* (1+ Breakeven Inflation)
Real Yield ~ Nominal Yield – Breakeven Inflation
base
cpi
ybase
cpi
ybase
cpi
ybase
cpi
yN
n
N
nnn
NN
22
1
1
M
1
C...
1
C
1
CP
– C is the periodic coupon payment– N is the number of years to maturity– M is the (face value) payment at maturity (100)– is nominal yield – Base is the cpi at the issue time– : cpi at time t
ny
tcpi
Inflation Market Inflation bond
Inflation Market Inflation bond
II. Inflation Products
80
0Index
TIndex Cumulative Inflation =
Cumulative Inflation-1
(1+X%) T -1
BUYER
Expected cashflows
SELLER
Inflation Products and Inflation Curve
Zero-coupon (ZC) inflation swap – indicative prices
The Buyer
– Receive Compounded Inflation at Maturity: CPIt/CPI0 -1
– Pay a known Fixed cash-flow at Maturity(1 + X%)^t -1
81
Inflation Products and Inflation Curve
Zero-coupon (ZC) inflation swap – indicative prices
Region Index Lag (if CPI) SettlementEurope CPI 3 months T+2France DRI T+2
UK DRI T+2US DRI T+2
82
Inflation Products and Inflation Curve
Zero-coupon (ZC) inflation swap –Market Convention
83
Inflation Products and Inflation CurveBuilding an inflation curve –Yearly tenor
For every year t:
• is calculated by the following formula :
• Base : CPI of reference for the swap curve ( 3m lag no
interpolate for EUR)
• : zero coupon inflation swap at maturity t
tt
t zcBPI )1()ase()(C t
tCPI
tzc
84
Inflation Products and Inflation Curve
Building an inflation curve –Yearly tenor
For every year t:
tt
t zcBPI )1()ase()(C t
• ZC : the inflation ZC swap curve is quoted in the inflation market
85
Inflation Products and Inflation Curve
Building an inflation curve –Yearly tenor
For every year t:
tt
t zcBPI )1()ase()(C t
• Base ( nov2013) :116.86
• We are in Fev14 with a 3m lag, the base is in nov13
86
Inflation Products and Inflation Curve
Building an inflation curve –seasonality vector
For monthly tenor: we need to incorporate seasonality
))]()([exp()(C)(C0
0t duusufPIPItT
T
Tt
• In year period of time we have
• We use the inflation swap rate f for the period [To;Tt ] :
012
1
i
is
))(exp(0
duuftT
T
87
Inflation Products and Inflation CurveBuilding an inflation curve –seasonality vector
For CPI(07/16), we have the following :
)exp(*)12
8exp((11/15) PI(07/16) PI 765432112
3 sssssssszc
CC
We are in Feb 2014 therefore inflation swap curve is base on nov 13 for the
eur inflation curve
is the 3yrs inflation zc swap rate
The seasonality from dec to july we add the item of our seasonality vector
where the base is equale to the cpi on
nov13 and is the 2yrs inflation zc swap rate
3zc
22 )1( base (11/15) PI ZCC 2zc
88
Inflation Products and Inflation CurveBuilding an inflation curve –seasonality vector
We define a seasonality vector using Eurostat model : http://sdw.ecb.europa.eu/browseTable.do?
ICP_ITEM=X02200&DATASET=0&node=2120778&REF_AREA=308&SERIES_KEY=122.ICP.M.U2.N.X022
00.4.INX&SERIES_KEY=122.ICP.M.U2.S.X02200.3.INX
89
Inflation Products and Inflation Curve
Building an inflation curve –seasonality vector
We can realize that the seasonality vector is getting
more and more strong over the years.
90
Expected cashflows
Inflation Products and Inflation Curve
Additive inflation swap & Real rate swap– indicative prices
X% + YoY InflationFloored @ 0.00%
Libor +/- margin
Client4.30%4.18%4.07%3.88%
2.77%
-4.90%-4.57%
-4.17%
-3.35%
-2.25%
Inflation Leg
Libor LegBank
YoY Inflation =
1
1tIndex
tIndex
91
– More balanced cashflow profile – It is a play on real rates
• Party A pays: YoY Inflation + X% vs Party B pays: Libor
X% is the real rate at the time of the trade• Party A is “receiver” in this real rate swap
– If you believe real rates are going to increase, you want to be Party A– If you believe real rates are going to decrease, you want to be Party B
– Widely traded by• Retail banks• Private banks• Asset managers• Corporates- as payer of
Inflation Products and Inflation CurveAdditive inflation swap & Real rate swap– indicative prices
92
Cumulative Inflation t =
0Index
tIndex
(1+X%) t -1
Cumulative Inflation t -1
Client
Expected cashflows
-2.83%
-5.80%-8.55%
-11.49%-14.44%
2.97%
5.89%8.64%
11.23%13.67%Inflation Leg
Fixed Leg
Bank
Inflation Products and Inflation CurveInflation-linked annuity swap– indicative prices
93
Combination of zero-coupon swaps with different maturities with additional constraint of having the same fixed rate for each swap
Hedges a periodic string of cashflows that increase with inflation each year – like rental income
Cashflows do not have to be the same
Widely traded by
Project finance linked entities
Insurance companies
Pension funds
Inflation Products and Inflation CurveInflation-linked annuity swap– indicative prices
94
At maturity: Inflation Uplift, Floored at 0%
Bond Coupons, paid on inflation-adjusted notional
Libor +/- asw margin
At inception: Dirty Price Adjustment (could be positive or negative)
Issuer
Inflation-linked BOND
Client Bank
Inflation Products and Inflation CurveInflation Asset Swap – Par-Par
95
Cumulative Inflation =
0Index
TIndex
At maturity:
100% * Max (Cumulative Inflation-1, 0.00%)
X% * Cumulative Inflation
Libor +/- asw margin
Client
Expected cashflows
-13.38%
-1.80%-1.75%-1.71%-1.68%
4.33%4.18%3.95%3.26%
2.23%
Inflation LegLibor Leg
Bank
Inflation Products and Inflation CurveInflation Asset Swap – Par-Par