1. http://pluto.huji.ac.il/~mswiener/zvi.html 972-2-588-3049 FRM Zvi Wiener Following P. Jorion, Financial Risk Manager Handbook Financial Risk Management

2. 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

3. Zvi Wiener slide 3 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

4. SwapsZvi Wiener slide 4 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.)

5. SwapsZvi Wiener slide 5 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%

6. SwapsZvi Wiener slide 6 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

7. SwapsZvi Wiener slide 7 Basic terms of IRS Notional amount Fixed rate leg Floating rate leg Calculated period Day count fraction

8. SwapsZvi Wiener slide 8 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!!

9. SwapsZvi Wiener slide 9 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.

10. SwapsZvi Wiener slide 10 Payments Fixed payment = (notional)(Fixed rate)(fixed rate day count convention) Floating payment = (notional)(Float. rate)(float. rate day count convention)

11. SwapsZvi Wiener slide 11 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

12. SwapsZvi Wiener slide 12

13. SwapsZvi Wiener slide 13 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

14. SwapsZvi Wiener slide 14 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.

15. SwapsZvi Wiener slide 15

16. SwapsZvi Wiener slide 16

17. SwapsZvi Wiener slide 17 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.

18. SwapsZvi Wiener slide 18 Zero coupon swap (reinvested payments) Amortizing swap (decreasing notional) Accreting swap (increasing notional) Rollercoaster (variable notional)

19. SwapsZvi Wiener slide 19 Amortizing swap Decreasing notional affects coupon payments

20. SwapsZvi Wiener slide 20 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!!

21. SwapsZvi Wiener slide 21 Unwinding Net of the two offsetting swaps is 2% for the life of the contract. (sometimes novation) AB 8% LIBOR AC 6% LIBOR

22. SwapsZvi Wiener slide 22 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

23. SwapsZvi Wiener slide 23 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.

24. SwapsZvi Wiener slide 24 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).

25. SwapsZvi Wiener slide 25 IRS Markets Daily average volume of trade (notional) 1995 1998 2001 $63B$155B$331B

26. SwapsZvi Wiener slide 26 Mark to market daily repricing collateral adjustments reduces credit exposure

27. SwapsZvi Wiener slide 27 Reasons to use swaps by firms Lower cost of funds Home market effects Comparative advantage of highly rated firms

28. SwapsZvi Wiener slide 28

29. SwapsZvi Wiener slide 29

30. SwapsZvi Wiener slide 30

31. SwapsZvi Wiener slide 31 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 = 30,000 All stocks and bonds = 70,000 Liquidation value = 2,800

32. SwapsZvi Wiener slide 32 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

33. SwapsZvi Wiener slide 33 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