Type of Document	Dissertation
Author	Tzigantcheva, Milena Gueorguieva
Author's Email Address	milena_t@hotmail.com
URN	etd-10182008-095740
Title	Stochastic Volatility Extensions of the Swap Market Model
Degree	Doctor of Philosophy
Department	Mathematics, Department of
Advisory Committee	Advisor Name Title Craig A. Nolder Committee Chair Alec Kercheval Committee Member Bettye Anne Case Committee Member De Witt Sumners Committee Member Jack Quine Committee Member Fred Huffer Outside Committee Member
Keywords	Swap Market Model Stochastic Volatility Extension Forward Swap Rate Fast Fractional Fourier Transform Swaption
Date of Defense	2008-10-08
Availability	unrestricted
Abstract 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.
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