# Numerical Computation of Theta in a Jump-Diffusion Model by Integration by Parts

1 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
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 European and Asian options with non-smooth payoff function. In time inhomogeneous models our formula applies to the derivative with respect to the maturity date $T$, and its proof can be viewed as a generalization of Dupire's integration by parts to arbitrary payoff functions. In the time homogeneous case, our result applies to the derivative with respect to the current date T, but our representation formula differs from the one obtained from the Black-Scholes PDE in terms of Delta and Gamma. Optimal weights are computed by minimization of variance and numerical simulations are presented.
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https://hal.inria.fr/inria-00070196
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Submitted on : Friday, May 19, 2006 - 7:27:37 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:07 PM
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• HAL Id : inria-00070196, version 1

### Citation

Delphine David, Nicolas Privault. Numerical Computation of Theta in a Jump-Diffusion Model by Integration by Parts. [Research Report] RR-5829, INRIA. 2006, pp.32. ⟨inria-00070196⟩

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