Quasi-Monte Carlo Methods in Numerical Finance

Corwin Joy, Phelim P. Boyle and Ken Seng Tan
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Corwin Joy: Enron Corporation, 1400 Smith Street, Houston, Texas 77002-7361
Phelim P. Boyle: School of Accountancy, University of Waterloo, Waterloo, Ontario N2L 3G1 Canada
Ken Seng Tan: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1 Canada

Management Science, 1996, vol. 42, issue 6, 926-938

Abstract: This paper introduces and illustrates a new version of the Monte Carlo method that has attractive properties for the numerical valuation of derivatives. The traditional Monte Carlo method has proven to be a powerful and flexible tool for many types of derivatives calculations. Under the conventional approach pseudo-random numbers are used to evaluate the expression of interest. Unfortunately, the use of pseudo-random numbers yields an error bound that is probabilistic which can be a disadvantage. Another drawback of the standard approach is that many simulations may be required to obtain a high level of accuracy. There are several ways to improve the convergence of the standard method. This paper suggests a new approach which promises to be very useful for applications in finance. Quasi-Monte Carlo methods use sequences that are deterministic instead of random. These sequences improve convergence and give rise to deterministic error bounds. The method is explained and illustrated with several examples. These examples include complex derivatives such as basket options, Asian options, and energy swaps.

Keywords: Monte Carlo simulation; quasi-random sequences; Faure sequences; numerical finance; derivative valuation (search for similar items in EconPapers)
Date: 1996
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