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arXiv · 2001.05531

Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation

G. Deligiannidis·S. Maurer·M. V. Tretyakov
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Abstract

We consider stochastic differential equations driven by a general L\'evy processes (SDEs) with infinite activity and the related, via the Feynman-Kac formula, Dirichlet problem for parabolic integro-differential equation (PIDE). We approximate the solution of PIDE using a numerical method for the SDEs. The method is based on three ingredients: (i) we approximate small jumps by a diffusion; (ii) we use restricted jump-adaptive time-stepping; and (iii) between the jumps we exploit a weak Euler approximation. We prove weak convergence of the considered algorithm and present an in-depth analysis of how its error and computational cost depend on the jump activity level. Results of some numerical experiments, including pricing of barrier basket currency options, are presented.

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G. Deligiannidis, S. Maurer, M. V. Tretyakov. 2020-01-15. Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation. https://doi.org/10.1007/s10543-021-00863-2

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