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Methods for Evaluating Density Functions of Exponential Functionals Represented as Integrals of Geometric Brownian Motion

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  • Kazuyuki Ishiyama

    (Nagoya University)

Abstract

The purpose of this paper is to present a survey on Yor's formula on the probability densities of the exponential functionals represented as integrals in time of geometric Brownian motions and to present results on numerical computations for the densities. We perform the computations via another formula for the densities obtained by Dufresne and we show numerically the desired coincidence in some cases. As an application, we compute the price of an Asian option.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:7:y:2005:i:3:d:10.1007_s11009-005-4517-9
    DOI: 10.1007/s11009-005-4517-9
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    References listed on IDEAS

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    1. Daniel Dufresne, 2000. "Laguerre Series for Asian and Other Options," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 407-428, October.
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    Cited by:

    1. Angelos Dassios & Luting Li, 2018. "An Economic Bubble Model and Its First Passage Time," Papers 1803.08160, arXiv.org.
    2. N. N. Leonenko & M. D. Ruiz-Medina, 2008. "Gaussian Scenario for the Heat Equation with Quadratic Potential and Weakly Dependent Data with Applications," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 595-620, December.
    3. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-24.
    4. 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.
    5. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," Papers 1505.06946, arXiv.org.

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