pratical fixed income_eisti 2015

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

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%


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


2) Flattening

Various possibilities :

rate

maturity

C1

C0

C1’

Higher short term rates

Lower long term rates


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

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


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


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


yx,FRA

FRA: Forward Rate Agreement

Value of the FRA formula :


)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


Yield100Price Future

Futures : Euribor3m

• Maturity 90 days

• Notional 1m

• K : numbers of contracts

• : Price of the Future at time t


)(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


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


FactorConversion

CCfundingCTD_BondCTD_Bond

Future

PricePrice


• 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 :


Future

CTD_Bond

Price

)(PV discountedYTMFactorConversion Future


• Issue 07/06/2014 : Bund Future =143

• CTD Price : YTM = 1.545


Future

CTD_Bond

Price

)(PV discountedYTMFactorConversion Future


• : Price at t0

• : Price at tf ( closing of the trade)

• K : Numbers of Contracts


)(100000& 0FFkLP f

0F

fF

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


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


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


Modified duration :

• Formula :

• Direct measure of price sensitivity to interest rate changes

y

DurationDm

1


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


Convexity Risk:

• Formula :

y

P

P

tty

CF

yy

P N

tt

t

2

2

1

222

2

1Convexity

)()1()1(

1


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


Example : DBR 4.75% 04/07/28


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


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


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

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


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


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


Building an inflation curve –Yearly tenor

For every year t:

tt


• ZC : the inflation ZC swap curve is quoted in the inflation market

85


Building an inflation curve –Yearly tenor

For every year t:

tt


• Base ( nov2013) :116.86

• We are in Fev14 with a 3m lag, the base is in nov13

86


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


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


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

pratical fixed income_eisti 2015

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