Stochastic Volatility Extensions of the Swap Market Model

Two stochastic volatility extensions of the SwapMarket Model, one with jumps and the other without,are derived. In both stochastic volatility extensionsof the Swap Market Model the instantaneous volatilityof the forward swap rates evolves according to asquare-root diffusion process. In the jump-diffusionstochastic volatility extension of the Swap MarketModel, the proportional log-normal jumps are appliedto the swap rates dynamics. The speed, theflexibility and the accuracy of the fast fractionalFourier transform made possible a fast calibration toEuropean swaption market prices. A specificfunctional form of the instantaneous swap ratevolatility structure was used to meet the observedevidence that volatility of the instantaneous swaprate decreases with longer swaption maturity and withlarger swaption tenors.