Financial Modeling & IT - Credit Risk & Swaps

7/31/2019 Financial Modeling & IT - Credit Risk & Swaps

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Credit Risk

KACZOROWSKA Natalia

MARRAI Gilles

PIERRE Corentin

Financial Modeling & IT

Part one :


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LOGO Table of Contents

1. Definition

2. Quantification of Credit Risk

1. Probability of default estimation

2. Default Probabilities and Equity prices3. Results in Matlab

3. Credit VaR

1. Introduction of the VaR

2. Credit VaR models

4. Credit Risk Losses

1. Estimating credit losses

2. Results in Matlab


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LOGO Definition

Credit risk is:

The risk that a loss will be experienced because of a default by the

counterparty in a derivatives transaction.

John C. Hull, Risk Management and Financial Institutions-2007


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LOGO Quantification of Credit Risk Probability of default

The Expected Default Losses:

Comparison between corporate bonds price with risk-free bonds price

Same maturity and same coupon

Usual assumption:

Spread between corporate and risk-free bond yields

PV of the cost of defaults is the excess of the price between a risk-free bond and acorporate bond


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LOGO

Example:

Bonds Value = 100

One-year risk-free bond (5%):

Similar corporate bond (5.25%) :

PV of the loss from default:

Expected default loss:

Quantification of Credit Risk Probability of default


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LOGO

Results:

Maturity (years) Risk-free zero rate (%)Corporate bond zero rate

(%)

Expected default loss (%

of no-default value)

1 5,00 5,25 0,2497

2 5,00 5,50 0,9950

3 5,00 5,70 2,0781

4 5,00 5,85 3,3428

5 5,00 5,95 4,6390



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LOGO

Probability of Default Assuming No Recovery:

Notations:

Y(T): Yield on a T-year corporate zero-coupon bond

Y*(T): Yield on a T-year risk-free zero-coupon bond

Q(T): Probability that corporation will default between time zero and time t



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LOGO

Bonds value: 100

PV of a risk-free zero-coupon bond:

PV of a similar corporate bond:

Expected loss from default:

The value of the bond with a default probability Q(T) :



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LOGO

The cumulative probability Q(T) is the same as the expected percentage loss

The probability of default is obtained by subtracting consecutive cumulative defaults

YearCumulative default probability (

% )

Default probability in year (

% )

1 0,2497 0.2497

2 0,9950 0.7453

3 2,0781 1.0831

4 3,3428 1.2647

5 4,6390 1.2962



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LOGO

The recovery rate R is the proportion of the claimed amount received in the event of adefault

In the event of a no default:

In the event of a default:

The value of the bond with a probability Q(T):



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LOGO

Strong assumptions:

The amount claimed in the event of a default equals the no-default value of the bond

The zero-coupon corporate bonds price are either calculable or observalble

Further:

Probabilities of default must be calculated from coupon-bearing bonds

The defaults can happen on any of the bond maturity dates



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LOGO

Merton Model (1974):

Companys equity is an option on the assets of the company

One zero-coupon bond matures at time T

Notation:

V0: Value of companys asset today

Vt: Value of the companys assets at time T

E0: Value of companys equity today

Et: Value of companys equity at time T

D : Amount of debt interest and principal due to be repaid at time TV : Volatility of assets (assumed constant)

E : Instantaneous volatility of equity

Quantification of Credit Risk Using equity prices


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LOGO

Thinking:

If VT< D: Default on the debt at time T equitys value = 0

If VT> D: Repayment at time T equitys value = VT D

Firms equity at time (ET) = max (VTD, 0) call option

Black-Scholes formula:

Where



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LOGO

As results:

The value of the debt today : V0 E0

The risk-neutral probability : N(-d2)

Requirement:

V0 and V are not directly observable

E0 and E are observable

Its lemma: EE0 = N(d1)VVO

Resolution:

Two equations that must be satisfied by V0 and V



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LOGO The CREDIT VaR - Introduction

The Value at Risk definition:

A loss that will not be exceeded at some specified confidence level

John C. Hull, Risk Management and Financial Institutions-2007

The Value at Risk interpretation:

We are X percent certain that we will not lose more than V dollars in the next N

days

V is the VaR of the portfolio,

N is the time horizon,

X is a the confidence level (usually 99.9%)


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LOGO

MARKET VaRs illustration:

We consider the change in the value of the portfolio

The distribution is the portfolios daily gain

The losses are counted as negative gains

The distribution approximately follows a normal law

Calculation of VaR from the probability distribution of the change in the portfolio

value; confidence level is X%

The CREDIT VaR - Introduction


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LOGO

CREDIT VaR is defined in the same way than MARKET VaR:

Credit VaR is the credit loss that will not be exceeded over some time horizon with a

specified confidence level

A creditVaR with a confidence level of 99.9% and a one-year time horizon is thecredit loss that we are 99.9% confident will not be exceeded over one year

However:

Time horizon for market Risk is usually between one day or one month

Time horizon for credit Risk is usually much longer-often one year

Several ways to calculate the credit VaR

Make the difference between trading book and banking book

The CREDIT VaR - Introduction


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LOGO The CREDIT VaR - The VaR Models

Important difference between trading book and banking book:

The 1996 Amendment (Basel Agreements) distinguishes between a banks trading

book and its banking book

The banking book:

It consists primarily of loans

Not marked to market (Fair Value) for managerial and accounting purposes

The trading book:

It consists of the myriad of different financial instruments

(stock, bonds, swaps, forward contract, exotic derivatives, etc.)

Instruments traded by the bank

Usually marked to market daily


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LOGO

For regulatory purposes- prescribed by the Basel Committee -:

Banks use the internal ratings based (IRB) approach

Banks have to calculate the credit VaR for items in the banking book

Vasiceks Model provides an easy way to estimate credit VaR for a loan portfolio

The VASICEKs Model:

Using a one-factor Gaussian copula model of time to default

There is a probability X that the percentage of defaults on a large portfolio by time is

less than

1

)()(),(

11XNTQN

NXTV

The CREDIT VaR - The VaR Models


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LOGO

The VASICEKs Model:

Q(T) is the cumulative probability of each loan

T is the time of default (usually 1 year)

Is the copula correlation

X is the confidence level (usually 99.9%)

Multiplied by the average exposure per loan and by the average loss given default

This gives the T-year VaR for an X% confidence level

1

)()(),(

11XNTQN

NXTV



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LOGO

Note about the copula correlation :

It is determined by the Basel Committee

It measures the correlation between each pair of obligors

It depends on the one-year probability of default

The formula is:

PDe 50112.0



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LOGO

Credit Risk Plus Model:

A similar approach for calculating credit VaR for the banking book

Used in the insurance industry

Proposed by Credit Suisse Financial Products in 1997

A simplified version of the approach is

Where

N is the number of counterparties

PD for each counterparty in time T is p

The expected number of default () for the whole portfolio is given by =Np

!n

en



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LOGO

Credit Risk Plus Model:

So the probability of n defaults is given by the Poisson distribution



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LOGO

The trading book involves a specific risk:

Specific risk is related to the credit quality of individuals companies

Banks use CreditMetrics model, proposed by J.P. Morgan in 1997

This involves simulating rating change for companies

Internal model with more freedom than standard VASICEKs Model

CreditMetrics is based on an analysis of credit migration

The probability to move between two rating categories during a period of time

Moodys proposed a ratings transition matrix



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LOGO

CreditMetrics Model:

This involves estimating a probability distribution of credit loss

This is simulating credit rating changes of all counterparties throughout the year

The credit loss is the difference between:

The credit rating at the beginning of the year

The credit rating at the end of the year

Rating transition matrix: Probabilities expressed as percentages

Aaa Aa A Baa Ba B Caa Default

A 0.05 2.39 91.83 5.07 0.5 0.13 0.01 0.02

B 0.01 0.03 0.13 0.43 6.52 83.20 3.04 6.64



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LOGO

Illustration:

We simulate the rating change of an A-rated and B-rated company (1-year)

The variable Xa determines the new rating of the company A

The variable Xb determines the new rating of the company B

Since for the company A:

N-1(0.0005)=-3.2905

N-1(0.0005+0.0239)=-1.9703

N-1(0.0005+0.0239+0.9183)=1.5779

The A-rated company gets upgraded to Aaa if Xa < -3.2905, Aa if -3.2905


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LOGO

Illustration:

And for the company B:

N-1(0.0001)=-3.7190

N-1(0.0001+0.0003)=-3.3528

N-1(0.0001+0.0003+0.0013)=-2.9290

The B-rated company gets upgraded to Aaa if Xb < -3.7190, Aa if -3.7190


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LOGO

Conclusion:

Calculate a one year VaR for portfolio using CreditMetrics involves:

Monte Carlo simulation of ratings transitions for bonds in the portfolio

On each simulation trial the final credit rating of all the bonds is calculated

The 99% worst results is the one-year 99% VaR



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LOGO

Note about the Monte Carlo simulation:

Suppose we wish to calculate a one-day VaR for a portfolio:

1. Value the portfolio today in the usual way using the current values of the market

variables

2. Sample once from the multivariate normal probability distribution of the Xi

3. Use the sampled values of the Xi to determine the value of each market

variable at the end of one day

4. Revalue the portfolio at the end of the day in the usual way

5. Substract the value calculated in Step 1 from the value in Step 4 to determine a

sample P

6. Repeat Steps 2 to 5 many times to buil up a probability distribution for P



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LOGO

Note about the Monte Carlo simulation:

The VaR is calculated as the appropriate percentile of the probability distribution of

P

For example:

We calculate 5000 different samples values ofP:

The one-day 99% VaR is the 50th worst outcome

The one-day 95% VaR is the 250th worst outcome



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LOGO Credit Risk Losses - Estimating Credit Losses

Before:

Probability of default (PD) & Recovery rate (R)

Now:

Estimation of the expected loss in the event of default

Known as the loss given defaultor LGD

A way to reduce contracts following the expected credit losses

The LGD on a loan is defined by:

The expected loss is PD x LGD


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LOGO

Derivatives transactions:

Credit exposure is more complicated on derivatives than on a loan

Claim within the event of a default is more uncertain than on a loan

Three possible situations:

1. The contract is always a liability to the financial institution

Short option position No claim, no credit risk

2. The contract is always an asset to the financial institution

Long option position Claim, credit risk

3. The contract can become either an asset or a liability

Forward contract or Swap Credit risk or not

Credit Risk Losses - Estimating Credit Losses


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LOGO

How to adjust the value of a derivative to allow for credit risk ?

The risk-neutral expected loss from default at time ti is

denotes expected value in a risk-neutral world

Taking present values leads to the cost of default:

Where is the value today of an instrument and



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LOGO

Consider again the three categories:

1. The contract is always a liability to the financial institution

The value of fi is always negative

The total expected loss from defaults is always zero

No adjustments for the cost of default

2. The contract is always an asset to the financial institution

The value of fi is always positive

The expression max(fi,0) is always equal to fi

Since vi is the present value of fi , it always equals f0

The expected loss from default is



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LOGO

Example:

Consider a two-year over-the-counter option with a value of $3

The probability of default is 4%

The recovery rate is 25%

The expected cost of defaults is

3 x 0.04 x (1 - 0.25) = $0.09

The buyer of the option should therefore be prepared to pay only $2.91

So the contract can be reduced following these expected credit losses



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LOGO

3. The contract can become either an asset or a liability

The sign of fi is uncertain

One way of calculating all the vi is to simulate the underlying market variables

over the life of the derivative

Another way can be a historical simulation approach



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LOGO

Consider a plain vanilla interest swap

Roughly done features of a plain vanilla swap:

A fixed rate of interest is exchanged for LIBOR

Both interest rates are applied to the same notional principal

A company A pays the LIBOR and receive a fixed rate of interest 5%

A company B pays a fixed rate of interest 5% and receives LIBOR



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LOGO

Features of contract for a company A:

Example from the book Risk Management & Financial institutionsby John C. Hull

Pays a fixed rate of interest of 5%

Receives LIBOR

Interest rates are reset every six months

The notional principal is $100

The swap lasts for three years

The swap is entered into on March 5, 2007 until on March 5, 2010



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LOGO

As results:

No adjustments for the cost of default for Mar. 2003 and Sep. 2003

Adjustment for the cost of default for Sep. 2004, Mar. 2005, Sep. 2005 and Mar. 2006



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SWAPS

KACZOROWSKA Natalia

MARRAI Gilles

PIERRE Corentin

Financial Modeling & IT

Part two :


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LOGO Table of Contents

1. Definition

2. Different types of Swaps

3. Swaps utilization

4. The Swaps Market

5. Swaps pricing

6. Swaps risks

7. Interest Rate Swap (Plain Vanilla interest rate swap)

8. Currency Swap

9. Commodity Swap

10. Credit Default Swap

11. Equity Swap

12. ISDA Documents


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LOGO Definition

Financial derivative

Agreement between 2 parties to exchange sequences of cash flows for a set period of

time

Benefits depend on the type of financial instrument involved Settlement dates

Settlement periods

Notional principal

Usually OTC lot of different structures and products (apart of certain type of swapssuch as CDS for instance)


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LOGO Different types of Swaps

Interest Rate swaps

Currency swaps

Commodity swaps

Credit Default swaps

Equity swaps

Others : Total return swap

Swaption (option on a swap)

Variance swap

Amortising swap Zero coupon swap

Deferred rate swap

Accreting swap

Forward swap


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LOGO Swaps utilization

Commercial needs

Comparative advantage

Acquiring certain types of financing (Convert financing into the desired type)

Fixed rate vs floating rate

Ex : a famous US company expansion in Europe

More favourable financing in US

Using a currency swap with better conditions

Hedging (interest rate risks, ...)

Speculate on changes in the expected direction of underlying prices


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LOGO The Swaps market

Usually used by firms and financial institutions

Few individuals


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LOGO Swaps pricing

Pricing a swap is calculating the fair fixed rate i.e. calculate a fixed rate whereby market

participants are indifferent between paying (receiving) this fixed rate over time or paying

(receiving) a rate that can fluctuate over time

This is accomplished by setting the value of the swap equal to zero at origination

This is achieved when the present value of the two (expected) cash flow streams equal each

other

Because a swap is equivalent to an asset and a liability, we can value each of them to

determine the value of the swap at any moment

Swaps can be priced using bonds because they can be seen as being in a long position in a

bond (in one currency, interest rate, ...) and short in another bond (other currency, other

interest rate, ...)

More generally, the cash-flow stream of a swap can often be considered as a stream of

forward contracts


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LOGO Swaps risks

Customized contracts Generally OTC market Entail credit risk

Potential losses from defaults on a swap are much less than the potential losses from defaults on

a loan with the same principal because, usually, the value of the swap is only a small part of the

value of the loan

Potential losses from defaults on a currency swap are usually greater than on a interest rate swapbecause the principal amounts in a currency swap are generally exchanged at the end of the life

of the swap which is not the case for a interest rate swap currency swap value are usually

greater than interest rate swap value


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LOGO Swaps risks

Swaps (especially OTC ones) might involve liquidity risk

Credit risk are not easy to hedge but market risk can be hedged by entering into

offsetting contracts i.e. Liquidate a futures position by entering an equivalent, but

opposite, transaction which eliminates the delivery obligation

The offsetting swap exactly counters the interest rate (or other market risk) of the

pre-existing swap but does not cancel the earlier swap (it does not eliminate all risk

of the earlier position)


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LOGO Swaps risks

Marketrisk

For the floating leg andfixed leg

Due to movement ofunderlyning index

(LIBOR)

Hedging by takingoffsetting positions insome combination of

currency futures, bond andinterest rate futures, currencyforward contracts,

spot currency and bond

markets

Creditrisk

For any counterparty

The exposure to the risk offailure of the other

counterparty

The cause OTC market,unstandardized products


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LOGO Interest Rate Swap

Interest rate cash flows exchange

Specified notional amount (generally not exchanged ; only for calculation)

Fixed rate Floating rate

Floating rate Fixed rate

Floating rate Another floating rate

Use for both hedging and speculating

Interest rate swap market : largest component of the global OTC derivative market

Notional amount outstanding 2009 (BIS) : $342 trillion

Gross Market Value : $13,9 trillion (06/2009)

Can be traded as an index through the FTSE MTIRS Index

A Plain vanilla swap is the most common type of swap. It is the exchange of a predetermined

fixed rate with a floating rate for the same period of time (and same notional)


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LOGO Interest Rate Swap - Example

Intel is currently paying floating interest rate but wants to pay fixed rate and Microsoft wants

the opposite

Party Intel agrees to pay Party Microsoft periodic fixed interest rate payments of 8,65%, in

exchange for periodic variable interest rate payments of LIBOR + 70 bps

Intel pays fixed rate to Microsoft called the swap rate (receives variable rate)

Microsoft pays floating rate to Intel indexed such as LIBOR (receives fixed rate)

Intel is called the payer

Microsoft is called the receiver

The nominal amount is $100 M

We can say that :

Microsoft has lent Intel $100M at 8,65%

Intel has lent Microsoft $100 M at LIBOR + 70 bps


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Floating interest rate

Floating interest rate

Fixed interest rate

Fixed interest rate

Initially

Finally

Note : LIBOR 03/01/2012 12M : 1,58357 %


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We can say that :

Microsoft has lent Intel $100M at 8,65%

Intel has lent Microsoft $100 M at LIBOR + 70 bps

Therefore, we can alo say that Microsoft has purchased a $100M floating-rate (LIBOR

+70bps) bond from Intel and sold a $100M fixed-rate (8,65%) bond to Intel

The value of the swap to Microsoft is therefore the difference between the values of 2 bonds


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LOGO Interest Rate Swap - Pricing

Formulas:

V = Bfix Bfl


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LOGO Currency Swap

Foreign exchange agreement

Exchange principal and/or interest in one currency for principal and/or interest in another

currency

Usually exchanged at the beginning and at the end of the life of the swap with the aim ofproviding financing in other currency

Motivated by comparative advantage

Main uses :

Secure cheaper debt

Hedge against exchange rate fluctuations


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LOGO Currency Swap - Example

Consider a 5-year currency swap agreement between IBM and British Petroleum entered

into on February 1, 2001

IBM :

Pays a fixed rate of interest of 11% in

Receives a fixed rate of interest of 8% in $

Interest rate payments are made once a year and the principal amounts are $15 million and

10 million

Fixed-for-fixed currency swap because the interest rate in both currency is fixed


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LOGO Currency Swap - Example

At the outset of the swap IBM pays $15 M and receives 10 M

Each year, IBM receives $1,2 M (8% of $15 m) and pays 1,1 (11% of 10 M)

At the end of the swaps life, IBM pays a principal of 10 M and receives a principal of $15 M

LOGO d


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LOGO Currency Swap Comparative advantage

Example :

Consider the 5-year fixed-rate borrowing costs to GM (USD) and QA (AUD)

AUD rates > USD rates

GM more creditworthy than QA (lower rates in both currencies)

Trader point of view : spread between the rates paid by GM and QA in the 2 markets are not the

same ; USD : QA - GM = 2% ; AUD : QA GM = 0,4%

GM have a comparative advantage in the USD market

QA have a comparative advantage in the AUD market

LOGO i d


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LOGO Currency Swap Comparative advantage

We suppose that GM wants to borrow 20 M AUD and QA wants to borrow 12 M USD

Currency exchange rate 0,6 USD/AUD

Perfect situation for a currency swap :

GM and QA each borrow in the market where they have a comparative advantage

GM borrows in the USD market

QA borrows in the AUD market

Then they use a currency swap to transform their loan into other currency

The total gain to all parties could be expected to be 2% - 0,4% = 1,6% per annum depending on the

swap used

LOGO C S V l i


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LOGO Currency Swap Valuation

If we consider the default risk t be inexistent, a currency swap can be decomposed in two

bonds

Consider the position of IBM in the previous example (after exchange of the principal)

It is short a GDP bond that pays 11% interest per annum and long a bond in USD that pays 8%

per annum

Vswap : value of the swap in USD (where USD are received and a foreign currency is paid)

BD is the value of the USD bond underlying the swap

BF is the value (measured in foreign currency) of the foreign-denominated bond underlying

the swap

S0 is the spot exchange

Vswap = BD - S0BF

If USD are paid and foreign currency is received, then Vswap = S0BF - BD

LOGO C S V l i


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LOGO Currency Swap Valuation

Example:

R Japan = 4% per annum

R USA = 9% per annum

Financial institution has entered into a currency swap in which it receives 5% per annum in yen and

pays 8% per annum in dollars once a year

The principals in 2 currencies are $10 M and 1,200 M yen

The swap lasts 3 years and the current exchange rate is 1$ = 110 yen

The value of the swap in dollar is then :

If the FI had been paying yen and receiving dollars, the value of the swap would have been 1.543

M dollars

LOGO C dit S


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LOGO Commodity Swap

Agreement whereby a floating (or market or spot) price based on an underlying commodity is

exchanged for a fixed price over a specific period

Similar to a fixed-for-floating interest rate swap

The difference is that in a fixed-for-floating interest rate swap the floating leg is based on

standard interest rates (e.g. Libor) where in a commodity swap the floating leg is based on the

price of the underlying commodity (e.g. oil or sugar)

No commodities are usually exchanged during the trade

The user of a commodity would secure a maximum price and would get payments based on the

market price for the commodity involved

On the other side, the producer of a commodity wishes to fix his income and to receive fixed

payments for the commodity

The vast majority of commodity swap involve oil

LOGO C dit S P i i


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LOGO Commodity Swap - Pricing

Si: spot price of a commodity at the beginning of period i

N : number of units of the commodity

X : fixed price for the commodity

M : total of payments (beginning one period from now)

Cash flow for the party that is long : CF = N*(0, S1-X, S2-X, ..., SM-X)

CF can be decomposed into a stream of fixed payments of NX that we can easily price and a

stochastic stream N(0, S1, S2, ..., SM)

The stochastic stream can be seen as to be equivalent to a stream of forward contracts on N

units of the commodity

Receiving N Si at period ihas the same value that receiving N Fiat time iwhere Fi is the date 0

forward price for delivery of one unit of the commodity at date i

and X is usually chosen so that the initial value of V is zero

LOGO C dit D f lt S


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LOGO Credit Default Swap

A CDS is an agreement in which the seller will compensate the buyer in the event of a loan

default

The buyer of the CDS makes a series of payments (the CDS fee or spread) to the seller and, in

exchange, receives a payoff if the loan default

In the event of default, the buyer receives the compensation (usually the face value of the

loan) and the seller takes possession of the defaulted loan

LOGO C dit D f lt S


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Outstanding CDS amount (end 2007) : $62,2 trillion

Outstanding CDS amount (mid-year 2010) : $26,3 trillion

Most CDS are documented using standard forms promulgated

by the International Swaps and Derivative Association (ISDA)

but some are tailored to meet specific needs

In addition to the basic single-name swaps, there are a lot of

other different swaps such as basket default swaps (BDS),

index CDS, funded CDS and loan-only CDS

LOGO Credit Defa lt S ap


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However, anyone can purchase a CDS even if he does not hold the loan instrument and who

has no direct insurable interest in the loan (called naked CDS); in that case, there is a

protocol to hold a credit event auction and the payment is usually substantially less than the

face value of the loan

The European Parliament has approved a ban on naked CDS since the end of 2011 but it only

applies to debt on sovereign nations

LOGO Credit Default Swap Risk


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LOGO Credit Default Swap - Risk

Systematic risk for the economy (multi-trillion dollar size of the market)

During the 2007-2010 financial crisis, the lack of transparency became a concern to regulators

Both buyer and seller of credit protection take on counterparty risk

The buyer takes risk that the seller may default

The seller takes risk that the buyer may default

The seller would try to hedge his exposure by buying an offsetting protection from another party

He could also sell the CDS to a third party but it could generate high losses

There is also a jump risk (or jump-to-default risk). The seller could expect a little probability of

default and if it appears, it creates a sudden obligation of payments for a substantial amount (could

be million of billion of $) which is not the case in other OTC derivatives.

There is a project to require the CDS to be traded and settled via a central exchange/clearing

house and there will no longer be counterparty risk as this risk will be held by that institution

CDS (especially OTC ones) might involve liquidity risk

LOGO Credit Default Swap and Insurance


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LOGO Credit Default Swap and Insurance

CDS could be compared with insurance. However, there are differences :

The main difference is simply that an insurance contract provides an indemnity against the losses

actually sufferedby the policy holder whereas the CDS provides an equal payout to all holders,

calculated using and agreed, market-wide method

There is also differences in the pricing approach. The cost of insurance is based on actuarial analysis .

CDS cost is determined using financial models and arbitrage relationships with other credit market

instruments (such as loans and bonds from the same reference entity)

The buyer of the CDS does not need to hold the underlying whereas for purchasing in insurance the

insured is expected to own a debt obligation

The seller of a CDs does not need to be a regulated entity

The seller is not always required to maintain any reserves to pay off the buyer (although major CDS

dealers are subject to bank capital requirement)

Insures manager risk primarily by setting loss reserves based on the Law of Large numbers while CDS

dealers manage risk primarily by means of offsetting CDS (hedging) with other dealers and

transactions in underlying bond markets

LOGO Credit Default Swaps Uses


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LOGO Credit Default Swaps - Uses

Speculation

Speculation on change on CDS spreads or of market indices (North American CDX index or European

iTraxx index)

If an investor believe that an entitys CDS spreads are too high or too low relative to the entitys bond yields and attempt to profit from that

view by entering into a trade, known as a basis trade, that combines a CDS with a cash bond and an interest rate swap

An investor might speculate on an entitys credit quality, since generally CDS spreads increase as

credit-worthiness decrease and decline as credit-worthiness increase. The investor might therefore

buy CDS protection on a company to speculate that it is about to default

Example:

An investor believes that Company A will soon default on its debt. Therefore, he buys $10 M worth of CDSprotection for two year from Bank B, with Company A as the reference entity, at a spread of 500 bps p.a

If Company A default after 1 year (for instance), the investor will have paid $500 000 and will make a profit of

$10M $500 000 = $9 500 000 and Bank B will incur a $9,5 M loss (unless it has offset its position)

If Company A does not default after the 2 year, the investor will have paid $1M and will therefore lose it totally

while Bank B will have a profit of the same amount



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Hedging

A bank for instance may hedge its risk that a borrower may default on a loan by entering in a CDS as

the buyer of protection

Another kind of hedge is against concentration risk. A banks risk manager may advise that the bank

is overly concentrated with a particular borrower or industry. The bank can then lay off some of this

risk by buying CDS. Because the borrower is not a party in the CDS, entering into it allows the bank

to achieve its diversity objectives

Similarly, a bank can sell CDS to diversify its portfolio by gaining exposure to an industry in which the

selling bank has no customer base

Most financial entitys think that using CDS as a hedging device has a useful purpose



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Hedging

Example:

A pension fund owns 5-year bonds issued by Company A with par value of $10 M

To manage the risk that Company A could defaults on its debt, the pension fund buys a CDSfrom Bank B for a notional amount of $10 M at a spread of 200 bps p.a.

If Company A does not default on its bond payments, the pension fund pays $200 000 a year

for 5 year ($1 M) and receives $10 M from Company A after that 5 years

If Company A defaults on its debt after 3 years (for instance), the pension fund would stop

paying its fees ($600 000 already paid) and is refunded with its $10 M - $600 000 = $9,4 M

LOGO Credit Default Swaps Pricing and Valuation


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The probability model :

4 inputs :

The issue premium

The recovery rate (% of notional repaid in event of default)

The credit curve (for the reference entity) The Libor curve

If no default : price of the CDS would be = sum of the discounted premium payments

Case of 1-year CDS with effective date t0 with 4 quarterly payments occurring at time t1, t2, t3 and t4

Nominal = N and issue premium = c (each quarterly payments = Nc/4)

For simplicity, we assume that defaults can only occur on one of the payment dates

5 ways that the contract could end:

No default : 4 premium payments made and the contract survive until maturity date

A default occurs on the first, second, third or fourth payment date



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OGO Credit Default Swaps Pricing and Valuation


We assign probability to

the 5 possible outcomes

and calculate the PV of the

payoff for each outcome

The PV of the CDS = PV of

the 5 payoffs * probability

of occurring

Probability of surviving over

the interval ti-1 to ti without

default is pi

Probability of default = 1-pi



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Credit Default Swaps Pricing and Valuation


Discount factor is

d

p1, p2, p3 and p4 are calculated using the credit spread curve

The probability of no default occurring between t and t + t decays exponentially with a time-

constant determined by the credit spread

Mathematically p = exp(-s(t)t/(1 R)) where s(t) is the credit spread zero curve at time t

The riskier the reference entity the greater the spread and the more rapidly the survival

probability decays over time



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Credit Default Swaps Pricing and Valuation


To get to total PV of the CDS we multiply the probability of each outcome by its present value to give

LOGO Equity Swap


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Equity Swap

The 2 parties make a series of payments to each other with at least one set of payments

determined by a stock or a index return

The other set of payments can be a fixed or floating rate or the return on another stock or

index

Equity swaps are used to substitute for a direct transaction in a stock

Equity swaps can avoid transaction costs (including tax) or locally based dividend taxes

There are different types of equity swap :

Equity return paid against a fixed rate

Equity return paid against a floating rate

Equity return paid against another equity return

LOGO Equity Swap


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Equity Swap

Example:

Equity return paid against a fixed rate

On 15/12/2000, Dynamic Money (US) enters into a swap for one year to pay a fixed rate of 5% and

receive the return on the S&P 500 with payments to occur on 15/03, 15/06, 15/09 15/12

The counterparty is Total Swaps, Inc. ; Notional amount : $20 M

The S&P 500 is at 1105.15 on the day the swap is initiated

The CF are as follow :

LOGO ISDA Documents


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ISDA Documents

The International Swaps and Derivatives Association (ISDA), founded in 1985, has worked to

make OTC derivatives markets safe and efficient

ISDAs pioneering work in developing the ISDA Master Agreement and a wide range of

related documentation materials, and in ensuring the enforceability of their netting and

collateral provisions, has helped to significantly reduce credit and legal risk

The ISDA netting act model defines all terms used in the ISDA Master Agreement or other

documents such as the cleared derivatives execution agreement, the Americas Interdealer

Master Equity Derivatives Confirmation Agreement, specific continents derivatives template,

ISDA Credit Derivatives Definitions or the pre-confirmation trade agreements.

LOGO ISDA Documents
http://isda%20documents/2006%20model%20netting%20act.pdfhttp://isda%20documents/ISDA%20Master%20Agreement%20Comerica%20bank%20and%20rackspace%20us%20inc..docxhttp://isda%20documents/http://isda%20documents/2004AmericasInterdealMEDCAgreement1.dochttp://isda%20documents/2004AmericasInterdealMEDCAgreement1.dochttp://isda%20documents/BRIC40Template.dochttp://isda%20documents/EXHIBIT-A-to-2003-ISDA-Credit-Derivatives-Definitions.dochttp://isda%20documents/http://isda%20documents/http://isda%20documents/http://isda%20documents/http://isda%20documents/EXHIBIT-A-to-2003-ISDA-Credit-Derivatives-Definitions.dochttp://isda%20documents/BRIC40Template.dochttp://isda%20documents/2004AmericasInterdealMEDCAgreement1.dochttp://isda%20documents/2004AmericasInterdealMEDCAgreement1.dochttp://isda%20documents/http://isda%20documents/ISDA%20Master%20Agreement%20Comerica%20bank%20and%20rackspace%20us%20inc..docxhttp://isda%20documents/2006%20model%20netting%20act.pdf


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ISDA Documents

The International Swaps and Derivatives Association launched in 2007 a standard template

for credit default swaps (CDS) on European leveraged loans, which are used by private equity

firms to fund buyouts.

The parties to the default swap can agree that a contract will be canceled if that loan is

subsequently refinanced. Alternatively, the contract will continue, referencing the new loans

used to refinance the original underlying obligation.

Standardization has proved to be a powerful force in the broader bond CDS market, leading

to the creation of benchmark traded indexes such as the iTraxx Crossover and Europe --

credit's equivalent of the FTSE 100 or Dow Jones industrial average.

ISDA provides both Standard Terms Supplement and Confirmation for European CDS.
http://www.reuters.com/finance/markets/index?symbol=us!djihttp://isda%20documents/iTraxx%C2%AE%20LevX%C2%AE%20Standard%20Terms%20Supplement%20for%20Credit%20Derivative%20Transactions%20on%20Leveraged%20Loans%20(Incorporating%20Auction%20Settlement).dochttp://isda%20documents/iTraxx%C2%AE%20LevX%C2%AE%20Confirmation%20for%20Credit%20Derivative%20Transactions%20on%20Leveraged%20Loans%20(Incorporating%20Auction%20Settlement).dochttp://isda%20documents/iTraxx%C2%AE%20LevX%C2%AE%20Confirmation%20for%20Credit%20Derivative%20Transactions%20on%20Leveraged%20Loans%20(Incorporating%20Auction%20Settlement).dochttp://isda%20documents/iTraxx%C2%AE%20LevX%C2%AE%20Confirmation%20for%20Credit%20Derivative%20Transactions%20on%20Leveraged%20Loans%20(Incorporating%20Auction%20Settlement).dochttp://isda%20documents/iTraxx%C2%AE%20LevX%C2%AE%20Standard%20Terms%20Supplement%20for%20Credit%20Derivative%20Transactions%20on%20Leveraged%20Loans%20(Incorporating%20Auction%20Settlement).dochttp://isda%20documents/iTraxx%C2%AE%20LevX%C2%AE%20Standard%20Terms%20Supplement%20for%20Credit%20Derivative%20Transactions%20on%20Leveraged%20Loans%20(Incorporating%20Auction%20Settlement).dochttp://www.reuters.com/finance/markets/index?symbol=us!dji