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

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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.

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Authors and Affiliations

  1. Graduate School of Human Informatics, Nagoya University, Chikusa-ku, Nagoya, 464-8601, Japan

    Kazuyuki Ishiyama

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  1. Kazuyuki Ishiyama
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Correspondence to Kazuyuki Ishiyama.

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AMS 2000 Subject Classification: 65C50, 60J65

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Ishiyama, K. Methods for Evaluating Density Functions of Exponential Functionals Represented as Integrals of Geometric Brownian Motion. Methodol Comput Appl Probab 7, 271–283 (2005). https://doi.org/10.1007/s11009-005-4517-9

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  • DOI: https://doi.org/10.1007/s11009-005-4517-9

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