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

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Title: An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients
Author(s): Chassagneux, J-F
Jacquier, A
Mihaylov, I
Item Type: Working Paper
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.
Publication Date: 20-Apr-2015
URI: http://hdl.handle.net/10044/1/29871
Copyright Statement: © 2015 The Authors
Keywords: q-fin.CP
q-fin.CP
math.NA
60H10
Computational finance
Numerical analysis
Appears in Collections:Financial Mathematics
Mathematics
Faculty of Natural Sciences



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