1. http://pluto.huji.ac.il/~mswiener/zvi.html 972-2-588-3049 FRM Chapter 22 Credit Derivatives Following P. Jorion 2001 Financial Risk Manager Handbook

2. Credit DerivativesZvi Wiener slide 2 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.

3. Credit DerivativesZvi Wiener slide 3 Credit Derivatives Bond insurance Letter of credit Credit derivatives on organized exchanges: TED spread = Treasury-Eurodollar spread (Futures are driven by AA type rates).

4. Credit DerivativesZvi Wiener slide 4 Types of Credit Derivatives Underlying credit (single or a group of entities) Exercise conditions (credit event, rating, spread) Payoff function (fixed, linear, non-linear)

5. Credit DerivativesZvi Wiener slide 5 Types of Credit Derivatives November 1, 2000 reported by Risk Credit default swaps45% Synthetic securitization26% Asset swaps12% Credit-linked notes9% Basket default swaps5% Credit spread options3%

6. Credit DerivativesZvi Wiener slide 6 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 - seller premium Contingent payment Reference asset

7. Credit DerivativesZvi Wiener slide 7 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.

8. Credit DerivativesZvi Wiener slide 8 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 ISDAs Master Netting Agreement

9. Credit DerivativesZvi Wiener slide 9 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).

10. Credit DerivativesZvi Wiener slide 10 Total Return Swap (TRS) A - buyer B - seller Payment tied to reference asset Payment tied to reference rate Reference asset

11. Credit DerivativesZvi Wiener slide 11 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

12. Credit DerivativesZvi Wiener slide 12 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

13. Credit DerivativesZvi Wiener slide 13 Credit Spread Option Put type Payment = Max(S-K, 0)*Duration*Notional Call type Payment = Max(K-S, 0)*Duration*Notional

14. Credit DerivativesZvi Wiener slide 14 Example A 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

15. Credit DerivativesZvi Wiener slide 15 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.

16. Credit DerivativesZvi Wiener slide 16 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.

17. Credit DerivativesZvi Wiener slide 17 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!

18. Credit DerivativesZvi Wiener slide 18 Types of Credit Linked Note TypeMaximal Loss Asset-backedInitial investment Compound CreditAmount from the first default Principal ProtectionInterest Enhanced Asset ReturnPre-determined

19. Credit DerivativesZvi Wiener slide 19 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

20. Credit DerivativesZvi Wiener slide 20 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 – it is worthless (the same default) C. Decreases in value only if the corporate bond is downgraded D. Is unchanged in value

21. Credit DerivativesZvi Wiener slide 21 FRM 2000-39 Credit Risk (22-5) 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

22. Credit DerivativesZvi Wiener slide 22 FRM 2000-39 Credit Risk 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 = $100*0.03*(1– 40%) only joint default leads to a loss D. None of the above

23. Credit DerivativesZvi Wiener slide 23 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

24. Credit DerivativesZvi Wiener slide 24 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 = [(12%-3%) –(11%+0.4%)]*$200M B. Net payment of $4.8M C. Net receipt of $5.2M D. Net payment of $5.2M

25. Credit DerivativesZvi Wiener slide 25 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 – Mertons model

26. Credit DerivativesZvi Wiener slide 26 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%.

27. Credit DerivativesZvi Wiener slide 27 Actuarial Method 1Y 1% probability of default 2Y: 0.01*0.90+0.02*0.07+0.05*0.02=1.14% StartingEnding stateTotal StateABCD A0.900.070.020.011.00 B0.050.900.030.021.00 C00.100.850.051.00 D0001.001.00

28. Credit DerivativesZvi Wiener slide 28 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):

29. Credit DerivativesZvi Wiener slide 29 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

30. Credit DerivativesZvi Wiener slide 30 Equity Price Method Following the Mertons 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