Error Bounds for Quasi-Monte Carlo Methods in Option Pricing

23 Pages Posted: 29 Dec 2004  

Jennifer X.F. Jiang

Northwestern University - Department of Industrial Engineering and Management Sciences

John R. Birge

University of Chicago - Booth School of Business

Date Written: December 13, 2004

Abstract

The classic error bounds for quasi-Monte Carlo approximation follow the Koksma-Hlawka inequality based on the assumption that the integrand has finite variation. Unfortunately, not all functions have this property. In particular, integrands for common applications in finance, such as option pricing, do not typically have bounded variation. In contrast to this lack of theoretical precision, quasi-Monte Carlo methods perform quite well empirically. This paper provides some theoretical justification for these observations. We present new error bounds for a broad class of option pricing problems using quasi-Monte Carlo approximation in one and multiple dimensions. The method for proving these error bounds uses a recent result of Niederreiter (2003) and does not require bounded variation or other smoothness properties.

Keywords: Error bounds, numerical integration, Quasi-Monte Carlo methods, option pricing

JEL Classification: C15, C44, G13

Suggested Citation

Jiang, Jennifer X.F. and Birge, John R., Error Bounds for Quasi-Monte Carlo Methods in Option Pricing (December 13, 2004). Available at SSRN: https://ssrn.com/abstract=634161 or http://dx.doi.org/10.2139/ssrn.634161

Xuefeng Jiang

Northwestern University - Department of Industrial Engineering and Management Sciences ( email )

Evanston, IL 60208-3119
United States

HOME PAGE: http://users.iems.nwu.edu/~xfjiang

John R. Birge (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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