Analytical Pricing of Swaption in Affine Term Structures with Stochastic Volatility

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 Fast Fourier Techniques (FFT) to price swaptions. Using ten years of swap rates and swaption premiums, model parameters are estimated using square-root unscented Kalman filter. We investigate the relationship between model premiums and interest rate factors, as well as market premiums and interest factors to conclude that long-dated swaptions are highly correlated to the shape of the curve.