Interest Rate Swap Valuation
14.1 CHAPTER OVERVIEW
This chapter explores the value of an IRS when the deal is first agreed, and methods for revaluing a swap given subsequent changes in market interest rates. It shows how a standard single currency fixed-floating swap can be priced as a combination of a straight bond and a floating rate note. It illustrates an alternative valuation methodology using forward interest rates, which can be used with standard swaps but also with a range of ‘non vanilla’ deals. A par IRS is one in which the present values of the fixed and floating legs are equal. The chapter shows how spot and forward rates can be extracted from the fixed rates on par swaps, using the bootstrapping method. The final sections explore how swaps can be priced and also hedged using interest rate futures.
14.2 VALUING A SWAP AT INCEPTION
The example is based on the case of a swap dealer who has just entered into an IRS on a notional $ 100 million with exactly three years from the start date to maturity. The payment legs are as follows:
• the dealer pays a fixed rate of 8 % p.a. annually in arrears;
• The dealer receives 12-month dollar LIBOR annually in arrears.
For simplicity it is assumed that interest payments on both the fixed and floating legs are calculated using the actual/actual day-count method. The cash flows are illustrated in Table 14.1
. At the end of each year the dealer pays $ 8 million and receives the LIBOR rate for that year applied to a notional principal ...