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Revisiting the numerical solution of stochastic differential equations

Revisiting the numerical solution of stochastic differential equations 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/approachThis paper develops a bias reducing method based loosely on extrapolation.FindingsThe 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/valueOverall, there is evidence to suggest that the proposed method is a viable, easy to implement competitor for other commonly used numerical schemes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png China Finance Review International Emerald Publishing

Revisiting the numerical solution of stochastic differential equations

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Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
2044-1398
DOI
10.1108/cfri-12-2018-0155
Publisher site
See Article on Publisher Site

Abstract

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/approachThis paper develops a bias reducing method based loosely on extrapolation.FindingsThe 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/valueOverall, there is evidence to suggest that the proposed method is a viable, easy to implement competitor for other commonly used numerical schemes.

Journal

China Finance Review International – Emerald Publishing

Published: Aug 16, 2019

Keywords: Monte Carlo simulation; Stochastic differential equations; C22; C52

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