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

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 Author David, Delphine ♦ Privault, Nicolas Source Hyper Articles en Ligne (HAL) Content type Text File Format PDF Language English
 Subject Keyword JUMP-DIFFUSION MODELS ♦ MALLIAVIN CALCULUS ♦ GREEKS ♦ THETA ♦ SENSITIVITY ANALYSIS ♦ info ♦ Computer Science [cs]/Other [cs.OH] 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. Educational Use Research Learning Resource Type Report ♦ Article Publisher Date 2006-01-01 Publisher Institution INRIA