1. http://pluto.huji.ac.il/~mswiener/zvi.html 972-2-588-3049 FRM Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html Swaps

2. Credit DerivativesZvi Wiener slide 2 Interest Rate Swaps: Concept An agreement between 2 parties to exchange periodic payments calculated on the basis of specified interest rates and a notional amount. Plain Vanilla Swap AB Fixed rate Floating rate Based on a presentation of Global Risk Strategy Group of Deutsche Bank

3. Credit DerivativesZvi Wiener slide 3 IRS In a standard IRS, one leg consists of fixed rate payments and the other depends on the evolution of a floating rate. Typically long dated contracts: 2-30 years Sometimes includes options, amortization, etc. Interest compounded according to different conventions (eg 30/360, Act/Act. Act/360, etc.)

4. Credit DerivativesZvi Wiener slide 4 IRS Origins AAA wants to borrow in floating and BBB wants to borrow in fixed. FixedFloating AAA7.00%LIBOR+5bps BBB8.50%LIBOR+85bps difference1.5%0.8% Net differential 70bps = 0.7%

5. Credit DerivativesZvi Wiener slide 5 Comparative Advantage Cost of funds for AAA=Libor - 40bp (45bps saved) Cost of funds for BBB=8.25% (25bps saved) Swap rate = 7.40% Swap rate is the fixed rate which is paid against receiving Libor. AAA BBB Libor 7.4% 7.0%Libor+85bp

6. Credit DerivativesZvi Wiener slide 6 Basic terms of IRS Notional amount Fixed rate leg Floating rate leg Calculated period Day count fraction

7. Credit DerivativesZvi Wiener slide 7 Basic terms of IRS Payer and receiver - quoted relative to fixed interest (i.e. payer = payer of fixed rate) buyer = payer, seller =receiver Short party = payer of fixed, (buyer) Long party = receiver of fixed, (seller) Valuation = net value NOT notional!!

8. Credit DerivativesZvi Wiener slide 8 Various swaps Coupon swaps - fixed against floating. Basis or Index swaps - exchange of two streams both are computed using floating IR. Currency swap - interest payments are denominated in different currencies. Asset swap - to exchange interest received on specific assets. Term swap maturity more then 2 years. Money Market swap - less then 2 years.

9. Credit DerivativesZvi Wiener slide 9 Payments Fixed payment = (notional)(Fixed rate)(fixed rate day count convention) Floating payment = (notional)(Float. rate)(float. rate day count convention)

10. Credit DerivativesZvi Wiener slide 10 Time Value of Money present value PV = CF t /(1+r) t Future value FV = CF t (1+r) t Net present value NPV = sum of all PV -PV5555105

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12. Credit DerivativesZvi Wiener slide 12 Swap Pricing A swap is a series of cash flows. An on-market swap has a Net Present Value of zero! PV(Fixed leg) + PV(Floating leg) = 0

13. Credit DerivativesZvi Wiener slide 13 Pricing Floating leg is equal to notional amount at each day of interest rate settlement (by definition of LIBOR). Fixed leg can be valued by standard NPV, since the paid amount is known.

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16. Credit DerivativesZvi Wiener slide 16 Forward starting swaps interest starts accruing at some date in the future. Valuation is similar to a long swap long and a short swap short.

17. Credit DerivativesZvi Wiener slide 17 Zero coupon swap (reinvested payments) Amortizing swap (decreasing notional) Accreting swap (increasing notional) Rollercoaster (variable notional)

18. Credit DerivativesZvi Wiener slide 18 Amortizing swap Decreasing notional affects coupon payments

19. Credit DerivativesZvi Wiener slide 19 Unwinding an existing swap Enter into an offsetting swap at the prevailing market rate. If we are between two reset dates the offsetting swap will have a short first period to account for accrued interest. It is important that floating payment dates match!!

20. Credit DerivativesZvi Wiener slide 20 Unwinding Net of the two offsetting swaps is 2% for the life of the contract. (sometimes novation) AB 8% LIBOR AC 6% LIBOR

21. Credit DerivativesZvi Wiener slide 21 Risks of Swaps Interest rate risk - value of fixed side may change Credit risk - default or change of rating of counterparty Mismatch risk - payment dates of fixed and floating side are not necessarily the same Basis risk and Settlement risk

22. Credit DerivativesZvi Wiener slide 22 Credit risk of a swap contract Default of counterparty (change of rating). Exists when the value of swap is positive Frequency of payments reduces the credit risk, similar to mark to market. Netting agreements. Credit exposure changes during the life of a swap.

23. Credit DerivativesZvi Wiener slide 23 Duration of a swap Fixed leg has a long duration (approximately). Short leg has duration about time to reset. Duration is a measure of price sencitivity to interest rate changes (approximately is equal to average time to payment).

24. Credit DerivativesZvi Wiener slide 24 IRS Markets Daily average volume of trade (notional) 1995 1998 2001 $63B$155B$331B

25. Credit DerivativesZvi Wiener slide 25 Mark to market daily repricing collateral adjustments reduces credit exposure

26. Credit DerivativesZvi Wiener slide 26 Reasons to use swaps by firms Lower cost of funds Home market effects Comparative advantage of highly rated firms

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30. Credit DerivativesZvi Wiener slide 30 FRM-GARP 00:47 Which one of the following deals has the largest credit exposure for a $1,000,000 deal size. Assume that the counterparty in each deal is a AAA-rated bank and there is no settlement risk. A. Pay fixed in an interest rate swap for 1 year B. Sell USD against DEM in a 1 year forward contract. C. Sell a 1-year DEM Cap D. Purchase a 1-year Certificate of Deposit

31. Credit DerivativesZvi Wiener slide 31 FRM-GARP 00:47 Which one of the following deals has the largest credit exposure for a $1,000,000 deal size. Assume that the counterparty in each deal is a AAA-rated bank and there is no settlement risk. A. Pay fixed in an interest rate swap for 1 year B. Sell USD against DEM in a 1 year forward contract. C. Sell a 1-year DEM Cap D. Purchase a 1-year Certificate of Deposit

32. Credit DerivativesZvi Wiener slide 32 Global Derivatives Markets 1999 IR contracts60,091 FRAs6,775 Swaps43,936 Options9,380 FX contracts14,344 Forwards9,593 Swaps2,444 Options2,307 Equity-linked contr.1,809 Forw. and swaps283 Options 1,527 Commodity contr.548 Others11,408 OTC Instruments $88T Exchange traded $13.5T IR contracts11,669 Futures7,914 Options3,756 FX contracts59 Futures37 Options22 Stock-index contr.1,793 Futures 334 Options 1,459 Source BIS World GDP in 99 = 30,000B All stocks and bonds = 70,000 Liquidation value = 2,800B

33. Credit DerivativesZvi Wiener slide 33 Global Derivatives Markets 2001 IR contracts77,513 FRAs7,737 Swaps58,897 Options10,879 FX contracts16,748 Forwards10,336 Swaps3,942 Options2,470 Equity-linked contr.1,881 Forw. and swaps320 Options 1,561 Commodity contr.598 Others14,375 OTC Instruments $111T Exchange traded $23.5T IR contracts21,614 Futures9,137 Options12,477 FX contracts89 Futures66 Options23 Stock-index contr.1,838 Futures 295 Options 1,543 Source BIS

34. 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

35. Credit DerivativesZvi Wiener slide 35 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.

36. Credit DerivativesZvi Wiener slide 36 Credit Derivatives Bond insurance Letter of credit Credit derivatives on organized exchanges: TED spread = Treasury-Eurodollar spread (Futures are driven by AA type rates).

37. Credit DerivativesZvi Wiener slide 37 Types of Credit Derivatives Underlying credit (single or a group of entities) Exercise conditions (credit event, rating, spread) Payoff function (fixed, linear, non-linear)

38. Credit DerivativesZvi Wiener slide 38 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%

39. Credit DerivativesZvi Wiener slide 39 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

40. Credit DerivativesZvi Wiener slide 40 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.

41. Credit DerivativesZvi Wiener slide 41 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

42. Credit DerivativesZvi Wiener slide 42 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).

43. Credit DerivativesZvi Wiener slide 43 Total Return Swap (TRS) A - buyer B - seller Payment tied to reference asset Payment tied to reference rate Reference asset

44. Credit DerivativesZvi Wiener slide 44 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

45. Credit DerivativesZvi Wiener slide 45 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

46. Credit DerivativesZvi Wiener slide 46 Credit Spread Option Put type Payment = Max(S-K, 0)*Duration*Notional Call type Payment = Max(K-S, 0)*Duration*Notional

47. Credit DerivativesZvi Wiener slide 47 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

48. Credit DerivativesZvi Wiener slide 48 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.

49. Credit DerivativesZvi Wiener slide 49 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.

50. Credit DerivativesZvi Wiener slide 50 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!

51. Credit DerivativesZvi Wiener slide 51 Types of Credit Linked Note TypeMaximal Loss Asset-backedInitial investment Compound CreditAmount from the first default Principal ProtectionInterest Enhanced Asset ReturnPre-determined

52. Credit DerivativesZvi Wiener slide 52 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

53. Credit DerivativesZvi Wiener slide 53 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

54. Credit DerivativesZvi Wiener slide 54 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

55. Credit DerivativesZvi Wiener slide 55 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

56. Credit DerivativesZvi Wiener slide 56 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

57. Credit DerivativesZvi Wiener slide 57 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

58. Credit DerivativesZvi Wiener slide 58 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

59. Credit DerivativesZvi Wiener slide 59 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%.

60. Credit DerivativesZvi Wiener slide 60 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

61. Credit DerivativesZvi Wiener slide 61 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):

62. Credit DerivativesZvi Wiener slide 62 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

63. Credit DerivativesZvi Wiener slide 63 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