Revisiting the numerical solution of stochastic differential equations

Abstract

Purpose

The purpose of this paper is to revisit the numerical solutions of stochastic differential equations (SDEs). An important drawback when integrating SDEs numerically is the number of steps required to attain acceptable accuracy of convergence to the true solution.

Design/methodology/approach

This paper develops a bias reducing method based loosely on extrapolation.

Findings

The method is seen to perform acceptably well and for realistic steps sizes provides improved accuracy at no significant additional computational cost. In addition, the optimal step size of the bias reduction methods is shown to be consistent with theoretical analysis.

Originality/value

Overall, there is evidence to suggest that the proposed method is a viable, easy to implement competitor for other commonly used numerical schemes.

Citation

Hurn, S., Lindsay, K.A. and Xu, L. (2019), "Revisiting the numerical solution of stochastic differential equations", China Finance Review International, Vol. 9 No. 3, pp. 312-323. https://doi.org/10.1108/CFRI-12-2018-0155