Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Chapter 44. Valuing a Plain Vanilla Swap

GERALD W. BUETOW, PhD, CFA

President and Founder of BFRC Services, LLC

FRANK J. FABOZZI, PhD, CFA, CPA

Professor in the Practice of Finance, Yale School of Management

Abstract: In an interest rate swap, the counterparties agree to exchange periodic interest payments. The dollar amount of the interest payments exchanged is based on the notional principal. In the most common type of swap, there is a fixed-rate payer (floating-rate receiver) and a fixed-rate receiver (floating-rate payer). The valuation of an interest rate swap requires the calculation of the present value of the swap payments that will be exchanged by the two parties. From the cash flow analysis of a swap, the swap rate is determined.

Keywords: interest rate swap, floating-rate payment, fixed-rate payment, swap rate, reference rate, notional amount, Eurodollar futures contract, forward discount factor, period forward rate

In this chapter, we will see how to value an interest rate swap and investigate the factors that affect a swap's value. Our focus is on a plain vanilla or generic interest rate swap assuming that the reference rate is the 3-month London Interbank Offered Rate (LIBOR). We begin by explaining how to compute the swap payments; this will take into account the number of days in a payment period based on day-count conventions commonly used in the bond market. Then we explain how to compute the present value of the swap payments and how to compute the swap fixed rate. ...