On Pricing and Hedging in the Swaption Market

Abstract

Values of interest rate derivatives, including swaps, caps and floors, and swaptions, are all determined by the term structure of interest in the market and its expected dynamics. The term structure encompasses interest rates at many maturities and, in principle, an interest-sensitive instrument is affected by all of them, as far into the future as the date of its final cash flow. There is no limit on the number of factors that can be incorporated into a theoretical pricing model, but practical considerations very much favor keeping the number down. In this article, Fan, Gupta, and Ritchken try to determine how many factors one really needs to build an adequate model for trading and hedging swaptions. They find that in pricing swaptions out-of-sample, a one-factor model works as well as a multifactor model with up to four factors, establishing along the way that it is quite important to allow volatility in the model to depend on the level of the underlying rates. However, hedging performance is quite different between one-factor and four-factor models, with the latter doing substantially better for risk management. <b>TOPICS:</b>Options, analysis of individual factors/risk premia, factor-based models