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Stochastic Volatility Extensions of the Swap Market Model
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Two stochastic volatility extensions of the Swap§Market Model, one with jumps and the other without,§are derived. In both stochastic volatility extensions§of the Swap Market Model the instantaneous volatility§of the forward swap rates evolves according to a§square-root diffusion process. In the jump-diffusion§stochastic volatility extension of the Swap Market§Model, the proportional log-normal jumps are applied§to the swap rates dynamics. The speed, the§flexibility and the accuracy of the fast fractional§Fourier transform made possible a fast calibration to§European swaption market prices. A specific§functional form of the instantaneous swap rate§volatility structure was used to meet the observed§evidence that volatility of the instantaneous swap§rate decreases with longer swaption maturity and with§larger swaption tenors.
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