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Exact Simulation of Occupation Times

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Monte Carlo and Quasi-Monte Carlo Methods 2010

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

Abstract

A novel algorithm for the exact simulation of occupation times for Brownian processes and jump-diffusion processes with finite jump intensity is constructed. Our approach is based on sampling from the distribution function of occupation times of a Brownian bridge. For more general diffusions we propose an approximation procedure based on the Brownian bridge interpolation of sample paths. The simulation methods are applied to pricing occupation time derivatives and quantile options under the double-exponential jump-diffusion process and the constant elasticity of variance (CEV) diffusion model.

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Acknowledgements

The first author acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) for a Discovery Research Grant. We thank the two anonymous reviewers for their comments, which helped to improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Roman N. Makarov & Karl Wouterloot

Authors
  1. Roman N. Makarov
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  2. Karl Wouterloot
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Correspondence to Roman N. Makarov .

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Editors and Affiliations

  1. , Institute of Applied Mathematics, University of Warsaw, Banacha 2, Warsaw, 02-097, Poland

    Leszek Plaskota

  2. , Institute of Applied Mathematics, University of Warsaw, Banacha 2, Warsaw, 02-097, Poland

    Henryk Woźniakowski

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Makarov, R.N., Wouterloot, K. (2012). Exact Simulation of Occupation Times. In: Plaskota, L., Woźniakowski, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2010. Springer Proceedings in Mathematics & Statistics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27440-4_33

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