Interest Rate Swaps & ED Futures Topic 12 Chapters 15, 16

1. Interest Rate Swaps & ED Futures Topic 12 Chapters 15, 16

2. Eurodollar futures contracts settle to LIBOR, which is a rate determined by obtaining quotes from a panel of banks. British Bankers Association (BBA)

3. Eurodollar Futures Prices

4. Eurodollar Futures Contract Specification

5. Convergence of Eurodollar Futures Prices to Libor Eurodollar futures prices settle to LIBOR. Specifically, Eurodollar futures prices settle to the 90-days LIBOR on the maturity date. This is shown below. For example, if LIBOR at maturity is 5%, then the ED futures price will be 100 x (1-0.05) = 95.00.

6. Implied Libor from ED futures prices While Eurodollar futures prices settle to LIBOR at maturity, There is no direct link between futures prices and LIBOR on other dates. However, we can compute the implied LIBOR from ED futures prices on other dates as follows. For example, if ED futures price is 94, then the implied LIBOR will be (1-94/100)x100=6%.

7. Convergence of Eurodollar Futures Prices to Libor

8. Eurodollar Futures Prices as of October 9th, 2006 are shown below. Spot Libor for maturity on 12/18/2006 stood at 5.40% (annualized).

9. Implied LIBOR as of October 9th, 2006 are shown below. Market’s best expectations of future LIBOR Implied LIBOR is the expected LIBOR (under the risk-neutral measure) that will prevail on the maturity date of the futures contract. It provides the fixed rate at which the investor is indifferent between receiving LIBOR or the fixed rate (as given by the implied LIBOR) when the contract matures.

10. What is the Swap rate on a swap that commences its first reset on 12/18/2006 and makes its last payment on 12/15/2008? Note that it is a 2-year swap with quarterly resets, and lagged payments following each reset. Assume that the fixed Swap rate payments are made on the dates indicated below

11. Estimating implied zero prices (discount rates) from ED Futures

12. Estimating forward swap rates from ED Futures Sample calculations: Floating payments on 3/19/2007: =F216*1000000*(B216-B215)/360 PV(Floating) on 3/19/2007: =G216*D216 Fixed on 6/18/2007: =K210*1000000/2 PV(Fixed) on 6/18/2007: =I217*D217

13. Interest Rate Swaps

14. Asset Swaps

15. Types of Swaps

16. Valuing Generic Interest Rate Swaps

17. Valuing Generic Interest Rate Swaps

18. Valuing Generic Interest Rate Swaps

19. Valuing Generic Interest Rate Swaps

20. Valuing Generic Interest Rate Swaps The sum of the present values of each floating payment is: 0.975 x 10.2564 + 0.945 x 12.6984 + 0.923 x 9.5341 + 0.914 x 3.9387 = 34.4000% The fixed payment that should be made each quarter, the sum of which will have the same present value, is 9.1563%, as shown in Table 16.4 . Hence the one-year swap rate as of October 28, 1999, is 9.1563%. The swap rate can also be obtained in Excel using the Solver function, as shown in Figure 16.4 .

21. Valuing Generic Interest Rate Swaps

22. Valuing Generic Interest Rate SwapsSwap rate as par bond yields One last point should be made concerning this example, which turns out to be much more general. Consider a one-year bond that pays 5.1563% every quarter and $1 at the end of one year. At what price should this bond sell on October 28, 2007? The sum of the present values of all quarterly fixed coupons plus the present value of final balloon payment of $1 is shown here:

23. Valuing Generic Interest Rate SwapsSwap rate as par bond yields This result, which is rather general, says that the coupon of a one-year bond that sells at par is in fact the generic swap rate. Since the coupon of a bond that sells at par is its yield to maturity, we can say that the generic swap rate of a swap with T years term is the T-year par bond yield .

24. Valuing Generic Interest Rate SwapsSwap rate as par bond yields

25. Valuing Generic Interest Rate SwapsSwap rate as par bond yields

26. Valuing Generic Interest Rate SwapsSwap rate as par bond yields

27. Theoretical Swap Rate • Formula for the Fixed Rate component of the swap contract:

28. Example of a swap • A municipal issuer and counterparty agree to a $100 million “plain vanilla” swap starting in January 2006 that calls for a 3-year maturity with the municipal issuer paying the Swap Rate (fixed rate) to the counterparty and the counter-party paying 6-month LIBOR (floating rate) to the issuer. Using the above formula, the Swap Rate can be calculated by using the 6-month LIBOR “futures” rate to estimate the present value of the floating component payments. Payments are assumed to be made on a semi-annual basis (i.e., 180-day periods). • The first step is to calculate the present value (PV) of the This is done by forecasting each semi-annual payment using the LIBOR forward (futures) rates for the next three years. The following table illustrates the calculations based on semi-annual payments

29. Example

30. As with the floating-rate payments, LIBOR forward rates are used to discount the notional principal for the 3 year period. The PV of the notional principal is calculated by multiplying the notional principal by the days in the period and the floating –rate forward discount factor.

32. Calculate the Swap Rate Theoretical Swap Rate = = 4.61% Based on the above example, the issuer (fixed-rate payer) will be willing to pay a fixed 4.61 percent rate for the life of the swap contact in return for receiving 6-month LIBOR. With a known Swap Rate, the counterparties can now determine the “swap spread.”4 The market convention is to use a U.S. Treasury security of comparable maturity as a benchmark. For example, if a three-year U.S. Treasury note had a yield to maturity of 4.31 percent, the swap spread in this case would be 30 basis points (4.61% - 4.31% = 0.30%).

33. Interest Rate Swap Spreads

34. Hedging Interest Rate Swap Positions

35. Hedging Interest Rate Swap Positions Implication: PV (Sum of Swap spreads) = PV (Sum of Libor – repo spreads)

36. Session - Conclusions/Main insights • Interest rate swaps have grown exponentially over the last two decades. • They are used by institutions to alter duration and to hedge interest rate risk. • Swap bid-offer spreads relate to the credit quality of swap intermediaries and counter-parties • Swaps can be priced using forward rates, or par bond yields. • Swap spreads over Treasury rates depend on LIBOR to repo rate spreads, liquidity factors and agency activities. • Interest rates swaps are collateralized and carry very little counter-party credit risk.