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Nicola Bruti-Liberati, Christina Nikitopoulos-Sklibosios, Eckhard Platen

First Order Strong Approximations of Jump Diffusions

Keywords: jump-diffusion processes, stochastic Taylor expansion, discrete time approximation, scenario simulation, first order strong convergence

This paper presents new results on strong numerical schemes, which are appropriate for scenario analysis, filtering and hedge simulation, for stochastic differential equations (SDEs) of jump-diffusion type. It provides first order strong approximations for jump-diffusion SDEs driven by Wiener processes and Poisson random measures. The paper covers first order derivative-free, drift-implicit and jump-adapted strong approximations. Moreover, it provides a commutativity condition under which the computational effort of first order strong schemes is independent of the total intensity of the jump measure. Finally, a numerical study on the accuracy of several strong schemes applied to the Merton model is presented.

Monte Carlo Methods and Applications, Walter de Gruyter

Print ISSN: 0929-9629
Volume: 12, 10/2006
Pages: 191 - 209

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