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

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.

36 pages, 17 figures, 2 tables

References in corpus (1)

• Strong convergence rates and temporal regularity for Cox-Ingersoll-Ross processes and Bessel processes with accessible boundaries

Cited by in corpus (5)

• On stochastic differential equations with arbitrary slow convergence rates for strong approximation
• On the Euler-Maruyama approximation for one-dimensional stochastic differential equations with irregular coefficients
• Adapted time steps explicit scheme for monotone BSDEs
• On hard quadrature problems for marginal distributions of SDEs with bounded smooth coefficients
• Convergence and qualitative properties of modified explicit schemes for BSDEs with polynomial growth