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Seminar on Probability and Statistics Tuesday August 22 2006 Tokyo 128 4:50-6:00 pm
A computation of Theta in a jump diffusion model by integration by parts
Delphine DAVID Departement de Mathematiques, Universite de La Rochelle 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.
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