Quasi-Monte Carol Methods for the Heston Model

Jan Baldeaux and Dale Roberts
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Dale Roberts: Australian National University

No 307, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: In this paper, we discuss the application of quasi-Monte Carlo methods to the Heston model. We base our algorithms on the Broadie-Kaya algorithm, an exact simulation scheme for the Heston model. As the joint transition densities are not available in closed-form, the Linear Transformation method due to Imai and Tan, a popular and widely applicable method to improve the effectiveness of quasi-Monte Carlo methods, cannot be employed in the context of path-dependent options when the underlying price process follows the Heston model. Consequently, we tailor quasi-Monte Carlo methods directly to the Heston model. The contributions of the paper are threefold: We firstly show how to apply quasi-Monte Carlo methods in the context of the Heston model and the SVJ model, secondly that quasi-Monte Carlo methods improve on Monte Carlo methods, and thirdly how to improve the effectiveness of quasi-Monte Carlo methods by using bridge constructions tailored to the Heston and SVJ models. Finally, we provide some extensions for computing greeks, barrier options, multidimensional and multi-asset pricing, and the 3=2 model.

Keywords: quasi-Monte Carlo methods; computational finance; stochastic volatility; path-dependent derivatives; bridge sampling; exact simulation (search for similar items in EconPapers)
Pages: 21 pages
Date: 2012-06-01
New Economics Papers: this item is included in nep-cmp
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp307.pdf (application/pdf)

Related works:
Working Paper: Quasi-Monte Carlo methods for the Heston model (2012)
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