Error Bounds for Quasi-Monte Carlo Methods in Option Pricing
23 Pages Posted: 29 Dec 2004
Date Written: December 13, 2004
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
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