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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…mehr

Produktbeschreibung
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.
Autorenporträt
Milena Tzigantcheva has an M.S. in Pure Mathematics from Sofia
University, Bulgaria and a Ph.D. in Financial Mathematics from
Florida State University. Milena is the Director of Risk
Management at the Florida State Board of Administration. She
currently lives in Tallahassee, Florida with her husband,
Dimitre, and their daughter, Adriana.