An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients

Jean-Francois Chassagneux; Antoine Jacquier; Ivo Mihaylov

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arXiv · 1405.3561

An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients

Jean-Francois Chassagneux·Antoine Jacquier·Ivo Mihaylov

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Abstract

We consider the approximation of stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler-Maruyama discretisation scheme that allows us to prove strong convergence, with a rate. Under some regularity and integrability conditions, we obtain the optimal strong error rate. We apply this scheme to SDEs widely used in the mathematical finance literature, including the Cox-Ingersoll-Ross~(CIR), the 3/2 and the Ait-Sahalia models, as well as a family of mean-reverting processes with locally smooth coefficients. We numerically illustrate the strong convergence of the scheme and demonstrate its efficiency in a multilevel Monte Carlo setting.

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Jean-Francois Chassagneux, Antoine Jacquier, Ivo Mihaylov. 2014-05-14. An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients. https://arxiv.org/abs/1405.3561

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