Seminar on Probability and Statistics

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Organizer(s) Nakahiro Yoshida, Hiroki Masuda, Teppei Ogihara, Yuta Koike

2006/08/22

16:50-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Delphine DAVID (Departement de Mathematiques, Universite de La Rochelle)
A computation of Theta in a jump diffusion model by integration by parts
[ Abstract ]
Using Malliavin weights in a jump-diffusion model we obtain an expression for Theta (the sensitivity of an option price with respect to the time remaining until exercise), with application to non-smooth payoff functions. Optimal weights are computed by minimization of variance and numerical simulations are presented for digital and European options. Some results are also presented for Asian options. Our representation formula for Theta differs in general from the one obtained from the Black-Scholes PDE in terms of Delta and Gamma.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/08.html