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Adaptive Simulation of the Heston Model

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  • Ian Iscoe
  • Asif Lakhany

Abstract

Recent years have seen an increased level of interest in pricing equity options under a stochastic volatility model such as the Heston model. Often, simulating a Heston model is difficult, as a standard finite difference scheme may lead to significant bias in the simulation result. Reducing the bias to an acceptable level is not only challenging but computationally demanding. In this paper we address this issue by providing an alternative simulation strategy -- one that systematically decreases the bias in the simulation. Additionally, our methodology is adaptive and achieves the reduction in bias with "near" minimum computational effort. We illustrate this feature with a numerical example.

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  • Ian Iscoe & Asif Lakhany, 2011. "Adaptive Simulation of the Heston Model," Papers 1111.6067, arXiv.org.
  • Handle: RePEc:arx:papers:1111.6067
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    File URL: http://arxiv.org/pdf/1111.6067
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    References listed on IDEAS

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    1. Hormann, W., 1993. "The transformed rejection method for generating Poisson random variables," Insurance: Mathematics and Economics, Elsevier, vol. 12(1), pages 39-45, February.
    2. 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.
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