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Exact simulation of Bessel diffusions

Author

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  • Makarov Roman N.

    (Department of Mathematics, Wilfrid Laurier University, 75 University Avenue West, Waterloo, Ontario, Canada. E-mail:)

  • Glew Devin

    (Department of Applied Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada. E-mail:)

Abstract

We consider the exact path sampling of the squared Bessel process and other continuous-time Markov processes, such as the Cox–Ingersoll–Ross model, constant elasticity of variance diffusion model, and confluent hypergeometric diffusions, which can all be obtained from a squared Bessel process by using a change of variable, time and scale transformation, and change of measure. All these diffusions are broadly used in mathematical finance for modeling asset prices, market indices, and interest rates. We show how the probability distributions of a squared Bessel bridge and a squared Bessel process with or without absorption at zero are reduced to randomized gamma distributions. Moreover, for absorbing stochastic processes, we develop a new bridge sampling technique based on conditioning on the first hitting time at the boundary of the state space. Such an approach allows us to simplify simulation schemes. New methods are illustrated with pricing path-dependent options.

Suggested Citation

  • Makarov Roman N. & Glew Devin, 2010. "Exact simulation of Bessel diffusions," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 283-306, January.
    • Handle: RePEc:bpj:mcmeap:v:16:y:2010:i:3-4:p:283-306:n:3
    DOI: 10.1515/mcma.2010.010
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    References listed on IDEAS

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    1. Devroye, Luc, 2002. "Simulating Bessel random variables," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 249-257, April.
    2. C. D. Kemp & Adrienne W. Kemp, 1991. "Poisson Random Variate Generation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 40(1), pages 143-158, March.
    3. Lin Yuan & John Kalbfleisch, 2000. "On the Bessel Distribution and Related Problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 438-447, September.
    4. Giuseppe Campolieti & Roman Makarov, 2007. "Pricing Path-Dependent Options On State Dependent Volatility Models With A Bessel Bridge," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 51-88.
    5. Giuseppe Campolieti & Roman Makarov, 2008. "Path integral pricing of Asian options on state-dependent volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 147-161.
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    Cited by:

    1. Jan Baldeaux & Dale Roberts, 2012. "Quasi-Monte Carol Methods for the Heston Model," Research Paper Series 307, Quantitative Finance Research Centre, University of Technology, Sydney.

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