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Bessel Processes and Asian Options

In: Numerical Methods in Finance

Author

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  • Daniel Dufresne

Abstract

The goal of this chapter is to give a concise account of the connection between Bessel processes and the integral of geometric Brownian motion. The latter appears in the pricing of Asian options. Bessel processes are defined and some of their properties are given. The known expressions for the probability density function of the integral of geometric Brownian motion are stated, and other related results are given, in particular the Geman and Yor (1993) Laplace transform for Asian option prices.

Suggested Citation

  • Daniel Dufresne, 2005. "Bessel Processes and Asian Options," Springer Books, in: Michèle Breton & Hatem Ben-Ameur (ed.), Numerical Methods in Finance, chapter 0, pages 35-57, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-25118-9_2
    DOI: 10.1007/0-387-25118-9_2
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    Citations

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    Cited by:

    1. Marjon Ruijter & Kees Oosterlee, 2012. "Two-dimensional Fourier cosine series expansion method for pricing financial options," CPB Discussion Paper 225, CPB Netherlands Bureau for Economic Policy Analysis.
    2. Leonardo Perotti & Lech A. Grzelak, 2021. "Fast Sampling from Time-Integrated Bridges using Deep Learning," Papers 2111.13901, arXiv.org.
    3. Friedrich Hubalek & Martin Keller-Ressel & Carlo Sgarra, 2014. "Geometric Asian Option Pricing in General Affine Stochastic Volatility Models with Jumps," Papers 1407.2514, arXiv.org.
    4. Park, Jong Jun & Jang, Hyun Jin & Jang, Jiwook, 2020. "Pricing arithmetic Asian options under jump diffusion CIR processes," Finance Research Letters, Elsevier, vol. 34(C).
    5. Anselm Hudde & Ludger Rüschendorf, 2023. "European and Asian Greeks for Exponential Lévy Processes," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-24, March.
    6. William T. Shaw, 2008. "A model of returns for the post-credit-crunch reality: Hybrid Brownian motion with price feedback," Papers 0811.0182, arXiv.org, revised Aug 2009.
    7. Marjon Ruijter & Kees Oosterlee, 2012. "Two-dimensional Fourier cosine series expansion method for pricing financial options," CPB Discussion Paper 225.rdf, CPB Netherlands Bureau for Economic Policy Analysis.
    8. William T. Shaw & Marcus Schofield, 2015. "A model of returns for the post-credit-crunch reality: hybrid Brownian motion with price feedback," Quantitative Finance, Taylor & Francis Journals, vol. 15(6), pages 975-998, June.

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