A Global Adaptive Quasi-Monte Carlo Algorithm for Functions of Low Truncation Dimension Applied to Problems from Finance

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 23)

Abstract

We show how to improve the performance of the quasi-Monte Carlo method for solving some pricing problems from financial engineering. The key point of the new algorithm, coined “GELT”, is an adaptive re-ordering of the point set so that the function is sampled more frequently in the regions where there is greater variation. The adaptivity only operates on the first few dimensions of the integrand and we show how to explicitly obtain the points of a digital sequence falling into boxes into these first few dimensions. This is effective as the problem is first transformed into having “low truncation dimension”. In general it is assumed that finance problems have low effective dimension. In addition we make use of a so-called “sniffer function” to cope with the discontinuity in the integrand function. Numerical results with the new adaptive algorithm are presented for pricing a digital Asian option, an Asian option and an Asian option with an up-and-out barrier.

Keywords

Monte Carlo Adaptive Algorithm Unit Cube Contingent Claim Brownian Bridge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors are grateful to Prof. Ian H. Sloan for useful discussions related to this paper and very much appreciated the careful comments and questions from the two anonymous referees. The first author is a fellow of the Research Foundation Flanders (FWO) and is grateful to the University of New South Wales where large parts of this paper were written; and therefore also thanks the Australian Research Council (ARC) for support.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Computer ScienceK.U.LeuvenHeverleeBelgium
  2. 2.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia

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