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

Chapter 45. Valuing Swaptions

FRANK J. FABOZZI, PhD, CFA, CPA

Professor in the Practice of Finance, Yale School of Management

GERALD W. BUETOW, PhD, CFA

President Founder of BFRC Services, LLC

Abstract: An interest rate swap is a derivative instrument wherein the counterparties agree to exchange periodic interest payments. In the generic interest rate swap, also referred to as the plain vanilla swap, one party (the fixed-rate payer) agrees to pay the other party fixed interest payments at designated dates for the life of the contract. The fixed rate that the fixed-rate payer must make is called the swap fixed rate or swap rate. The other party agrees to make payments that float with some reference rate (the fixed-rate receiver). There are options on interest rate swaps, referred to as swaptions. There are two types of swaps: a pay fixed swaption and a received fixed swaption. As the name implies, the former swaption entitles the option buyer to enter into an interest rate swap in which the buyer of the option pays a fixed rate and receives a floating rate; the latter swaption grants the buyer the right to enter into an interest rate swap that requires paying a floating rate and receiving a fixed rate. While the valuation of a plain vanilla interest rate swaps is straightforward, the valuation of swaptions is more complex.

Keyword: interest rate swap, plain vanilla swap, swaptions, pay fixed swaption, pay floating swaption, lattice model, interest rate models, backward induction

The valuation ...