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Monte Carlo Computation of the Laplace Transform of Exponential Brownian Functionals

Author

Listed:
  • Nicolas Privault

    (Nanyang Technological University)

  • Wayne Isaac Uy

    (Nanyang Technological University)

Abstract

This paper is concerned with the Monte Carlo numerical computation of the Laplace transform of exponential Brownian functionals. In addition to the implementation of standard integral formulas, we investigate the use of various probabilistic representations. This involves in particular the simulation of the hyperbolic secant distribution and the use of several variance reduction schemes. The performance of those methods and their conditions of application are compared.

Suggested Citation

  • Nicolas Privault & Wayne Isaac Uy, 2013. "Monte Carlo Computation of the Laplace Transform of Exponential Brownian Functionals," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 511-524, September.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:3:d:10.1007_s11009-011-9261-8
    DOI: 10.1007/s11009-011-9261-8
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    References listed on IDEAS

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    1. Vadim Linetsky, 2004. "Spectral Expansions for Asian (Average Price) Options," Operations Research, INFORMS, vol. 52(6), pages 856-867, December.
    2. Kazuyuki Ishiyama, 2005. "Methods for Evaluating Density Functions of Exponential Functionals Represented as Integrals of Geometric Brownian Motion," Methodology and Computing in Applied Probability, Springer, vol. 7(3), pages 271-283, September.
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    Cited by:

    1. Dan Pirjol & Lingjiong Zhu, 2023. "Asymptotics for the Laplace transform of the time integral of the geometric Brownian motion," Papers 2306.09084, arXiv.org.

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