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First Order Strong Approximations of Jump Diffusions

Nicola Bruti-Liberati, Christina Nikitopoulos-Sklibosios () and Eckhard Platen ()

Monte Carlo Methods and Applications, 2006, vol. 12, issue 3, 191-209

Abstract: 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.

Date: 2006
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DOI: 10.1515/156939606778705191

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