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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.
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.