Pricing of Swaptions in Affine Term Structures with Stochastic Volatility

Abstract

In an affine term structure framework with stochastic volatility, we derive the characteristic function of the log swap rate. Having the characteristic function, we employ the fast Fourier transform (FFT) to price swaptions. Using ten years of swap rates and swaption premiums, model parameters are estimated using a square-root unscented Kalman filter. We investigate the relationship between model premiums and interest rate factors, as well as between market premiums and interest factors, to conclude that long-dated swaptions are highly correlated to the shape of the curve.

Linearity-Generating Processes, Unspanned Stochastic Volatility, and Interest-Rate Option Pricing

“…This is not the case for the exponential affine or quadratic class. Researchers often resort to different dynamics specifications for pricing caps and floors, which are essentially options on zero-coupon bond, than for pricing swaptions; or one must resort to linear approximations to retain tractability (Heidari, Hirsa, and Madan (2007) and Schrager and Pelsser (2006)). By starting with a linearity-generating process, we remove the need for linear approximation on the pricing relation and circumvent the concern on internal consistency when different dynamics or different approximations are used to price different contracts.…”