Financial Risk Management

http://pluto.huji.ac.il/~mswiener/zvi.html

972-2-588-3049FRM

Zvi WienerFollowing

P. Jorion, Financial Risk Manager Handbook

Financial Risk Management

http://pluto.huji.ac.il/~mswiener/zvi.html

972-2-588-3049FRM

Chapter 22Credit Derivatives

Following P. Jorion 2001

Financial Risk Manager Handbook

Zvi Wiener slide 3Ch. 22, Handbook

Credit Derivatives

From 1996 to 2000 the market has grown from

$40B

to

$810B

Contracts that pass credit risk from one counterparty to

another. Allow separation of credit from other exposures.


Credit Derivatives

Bond insurance

Letter of credit

Credit derivatives on organized exchanges:

TED spread = Treasury-Eurodollar spread

(Futures are driven by AA type rates).


Types of Credit Derivatives

Underlying credit (single or a group of entities)

Exercise conditions (credit event, rating, spread)

Payoff function (fixed, linear, non-linear)


Types of Credit Derivatives

November 1, 2000 reported by Risk

Credit default swaps 45%

Synthetic securitization 26%

Asset swaps 12%

Credit-linked notes 9%

Basket default swaps 5%

Credit spread options 3%


Credit Default Swap

A buyer (A) pays a premium (single or periodic

payments) to a seller (B) but if a credit event

occurs the seller (B) will compensate the buyer.

A - buyer B - sellerpremium

Contingent payment

Reference asset


Example• The protection buyer (A) enters a 1-year credit

default swap on a notional of $100M worth of 10-year

bond issued by XYZ. Annual payment is 50 bp.

• At the beginning of the year A pays $500,000 to the

seller.

• Assume there is a default of XYZ bond by the end

of the year. Now the bond is traded at 40 cents on

dollar.

• The protection seller will compensate A by $60M.


Types of Settlement

Lump-sum – fixed payment if a trigger event occurs

Cash settlement – payment = strike – market value

Physical delivery – you get the full price in exchange

of the defaulted obligation.

Basket of bonds, partial compensation, etc.

Definition of default event follows ISDA’s Master

Netting Agreement


Total Return Swap (TRS)

Protection buyer (A) makes a series of payments

linked to the total return on a reference asset. In

exchange the protection seller makes a series of

payments tied to a reference rate (Libor or

Treasury plus a spread).


Total Return Swap (TRS)

A - buyer B - sellerPayment tied to reference asset

Payment tied to reference rate

Reference asset


Example TRS• Bank A made a $100M loan to company XYZ at a fixed rate

of 10%. The bank can hedge the exposure to XYZ by entering

TRS with counterparty B. The bank promises to pay the

interest on the loan plus the change in market value of the loan

in exchange for LIBOR + 50 bp.

• Assume that LIBOR=9% and by the end of the year the value

of the bond drops from $100 to $95M.

• The bank has to pay $10M-$5M=5M and will receive in

exchange $9+$0.5M=9.5M


Credit Spread Forward

Payment = (S-F)*Duration*Notional

S – actual spread

F – agreed upon spread

Cash settlement

May require credit line of collateral

Payment formula in terms of prices

Payment =[P(y+F, T)-P(y+S,T)]*Notional


Credit Spread OptionPut type

Payment = Max(S-K, 0)*Duration*Notional

Call type

Payment = Max(K-S, 0)*Duration*Notional


ExampleA credit spread option has a notional of $100M with a maturity of

one year. The underlying security is a 8% 10-year bond issued by

corporation XYZ. The current spread is 150bp against 10-year

Treasuries. The option is European type with a strike of 160bp.

Assume that at expiration Treasury yield has moved from 6.5% to

6% and the credit spread widened to 180bp.

The price of an 8% coupon 9-year semi-annual bond discounted at

6+1.8=7.8% is $101.276.

The price of the same bond discounted at 6+1.6=7.6% is $102.574.

The payout is (102.574-101.276)/100*$100M = $1,297,237


Credit Linked Notes (CLN)

Combine a regular coupon-paying note with some

credit risk feature.

The goal is to increase the yield to the investor in

exchange for taking some credit risk.


CLN

A buys a CLN, B invests the money in a high-

rated investment and makes a short position in a

credit default swap.

The investment yields LIBOR+Ybp, the short

position allows to increase the yield by Xbp, thus

the investor gets LIBOR+Y+X.


Credit Linked Note

Credit swap buyer

investor

AAA asset

CLN =

AAA note +

Credit swap

par

L+X+Y

Contingent payment

Xbp

Contingent payment

par LIBOR+Y

Asset backed securities can be very dangerous!


Types of Credit Linked Note

Type Maximal Loss

Asset-backed Initial investment

Compound Credit Amount from the first default

Principal Protection Interest

Enhanced Asset Return Pre-determined


FRM 1999-122 Credit Risk (22-4)

A portfolio manager holds a default swap to hedge an AA

corporate bond position. If the counterparty of the default

swap is acquired by the bond issuer, then the default swap:

A. Increases in value

B. Decreases in value

C. Decreases in value only if the corporate bond is

downgraded

D. Is unchanged in value



A portfolio manager holds a default swap to hedge an AA

corporate bond position. If the counterparty of the default

swap is acquired by the bond issuer, then the default swap:

A. Increases in value

B. Decreases in value – it is worthless (the same default)

C. Decreases in value only if the corporate bond is

downgraded

D. Is unchanged in value



A portfolio consists of one (long) $100M asset and a default

protection contract on this asset. The probability of default over the

next year is 10% for the asset, 20% for the counterparty that wrote

the default protection. The joint probability of default is 3%.

Estimate the expected loss on this portfolio due to credit defaults

over the next year assuming 40% recovery rate on the asset and 0%

recovery rate for the counterparty.

A. $3.0M

B. $2.2M

C. $1.8M

D. None of the above


FRM 2000-39 Credit RiskA portfolio consists of one (long) $100M asset and a default

protection contract on this asset. The probability of default over the

next year is 10% for the asset, 20% for the counterparty that wrote

the default protection. The joint probability of default is 3%.

Estimate the expected loss on this portfolio due to credit defaults

over the next year assuming 40% recovery rate on the asset and 0%

recovery rate for the counterparty.

A. $3.0M

B. $2.2M

C. $1.8M = $100*0.03*(1– 40%) only joint default leads to a loss

D. None of the above



Bank made a $200M loan at 12%. The bank wants to hedge the

exposure by entering a TRS with a counterparty. The bank promises

to pay the interest on the loan plus the change in market value in

exchange for LIBOR+40bp. If after one year the market value of

the loan decreased by 3% and LIBOR is 11% what is the net

obligation of the bank?

A. Net receipt of $4.8M

B. Net payment of $4.8M

C. Net receipt of $5.2M

D. Net payment of $5.2M



Bank made a $200M loan at 12%. The bank wants to hedge the

exposure by entering a TRS with a counterparty. The bank promises

to pay the interest on the loan plus the change in market value in

exchange for LIBOR+40bp. If after one year the market value of

the loan decreased by 3% and LIBOR is 11% what is the net

obligation of the bank?

A. Net receipt of $4.8M = [(12%-3%) –(11%+0.4%)]*$200M

B. Net payment of $4.8M

C. Net receipt of $5.2M

D. Net payment of $5.2M


Pricing and Hedging Credit Derivatives

1. Actuarial approach – historic default rates

relies on actual, not risk-neutral probabilities

2. Bond credit spread

3. Equity prices – Merton’s model


Example: Credit Default Swap

CDS on a $10M two-year agreement.

A – protection buyer agrees to pay to

B – protection seller a fixed annual fee in exchange for protection against default of 2-year bond XYZ.

The payout will be Notional*(100-B) where B is the price of the bond at expiration, if the credit event occurs.

XYZ is now A rated with YTM=6.6%, while T-note trades at 6%.


Actuarial Method

1Y 1% probability of default

2Y: 0.01*0.90+0.02*0.07+0.05*0.02=1.14%

Starting Ending state TotalState A B C DA 0.90 0.07 0.02 0.01 1.00B 0.05 0.90 0.03 0.02 1.00C 0 0.10 0.85 0.05 1.00D 0 0 0 1.00 1.00


Actuarial Method

1Y 1% probability of default

2Y: 0.01*0.90+0.02*0.07+0.05*0.02=1.14%

If the recovery rate is 60%, the expected costs are

1Y: 1%*(100%-60%) = 0.4%

2Y: 1.14%*(100%-60%) = 0.456%

Annual cost (no discounting):

800,42$%)60%100(2

%14.1%110$

M


Credit Spread Method

Compare the yield of XYZ with the yield of

default-free asset. The annual protection cost is

Annual Cost = $10M (6.60%-6%) = $60,000


Equity Price Method

Following the Merton’s model (see chapter 21) the fair value of the Put is

The annual protection fee will be the cost of Put divided by the number of years.

To hedge the protection seller would go short the following amount of stocks

)()( 21 dNKedNVPut rT

)(

11

1dNS

V

V

Put

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