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