Management

Credit Derivatives

Following P. Jorion, Financial Risk Management Chapter 22

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Credit Derivatives

From 1996 to 2000 the market has grown from

$40B

to

$810B

Contracts that pass from one counterparty to another. Allow separation of credit from other exposures.

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Page 1 1 Credit Derivatives

Bond

Letter of credit

Credit derivatives on organized exchanges:

TED spread = Treasury-Eurodollar spread

(Futures are driven by AA type rates).

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Types of Credit Derivatives

Underlying credit (single or a group of entities)

Exercise conditions (credit event, rating, spread)

Payoff function (fixed, linear, non-linear)

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Page 2 2 Types of Credit Derivatives

November 1, 2000 reported by Risk Credit swaps 45% Synthetic 26% Asset swaps 12% Credit-linked notes 9% Basket default swaps 5% options 3%

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Credit Default Swap

A buyer (A) pays a premium (single or periodic ) to a seller (B) but if a credit event occurs the seller (B) will compensate the buyer.

premium A - buyer B - seller Contingent Reference asset

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Page 3 3 Example

 The protection buyer (A) enters a 1-year on a notional of $100M worth of 10-year 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.

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Types of Settlement

Lump-sum – fixed payment if a trigger event occurs 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

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Page 4 4 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).

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Total Return Swap (TRS)

Payment tied to reference asset A - buyer B - seller Payment tied to reference rate Reference asset

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Page 5 5 Example TRS

 A made a $100M to company XYZ at a fixed rate of 10%. The bank can 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

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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

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Page 6 6 Credit Spread

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

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

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Example

A credit spread option has a notional of $100M with a maturity of one year. The underlying 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 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

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Page 7 7 Credit Linked Notes (CLN)

Combine a regular coupon-paying note with some credit risk feature.

The goal is to increase the yield to the in exchange for taking some credit risk.

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CLN

A buys a CLN, B invests the money in a high- rated investment and makes a 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.

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Page 8 8 Credit Linked Note

par Xbp CLN = Credit swap L+X+Y investor buyer AAA note + Credit swap Contingent payment Contingent payment

par LIBOR+Y

AAA asset

Asset backed securities can be very dangerous!

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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

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Page 9 9 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

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FRM 2000-39 Credit Risk (22-5)

A portfolio consists of one () $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

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Page 10 10 FRM 2000-62 Credit Risk (22-11)

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

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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

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Page 11 11 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%.

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Actuarial Method

Starting Ending state Total State A B C D A 0.90 0.07 0.02 0.01 1.00 B 0.05 0.90 0.03 0.02 1.00 C 0 0.10 0.85 0.05 1.00 D 0 0 0 1.00 1.00 1Y 1% probability of default 2Y: 0.01*0.90+0.02*0.07+0.05*0.02=1.14%

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Page 12 12 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): 1% + 14.1 % $10 M (100 % − 60 %) = $42 ,800 2

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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

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Page 13 13 Equity Price Method

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

Put = −V ⋅ N −d + Ke −rT ⋅ N d ( 1) ( 2 ) 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 ∂Put ∂V 1 =1− ∂V ∂S N d ( 1)

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