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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 rate 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.
A Dissertation Submitted to the Department of Mathematics in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy.
Includes bibliographical references.
Florida State University
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