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Quasi-Monte Carlo methods for the Heston model

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  • Jan Baldeaux
  • Dale Roberts

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.

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  • Jan Baldeaux & Dale Roberts, 2012. "Quasi-Monte Carlo methods for the Heston model," Papers 1202.3217, arXiv.org, revised May 2012.
    • Handle: RePEc:arx:papers:1202.3217
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    Cited by:

    1. Pierre-Antoine Arsaguet & Paul Bilokon, 2023. "Derivatives Sensitivities Computation under Heston Model on GPU," Papers 2309.10477, arXiv.org.
    2. Wenbin Hu & Junzi Zhou, 2017. "Backward simulation methods for pricing American options under the CIR process," Quantitative Finance, Taylor & Francis Journals, vol. 17(11), pages 1683-1695, November.
    3. T. Pellegrino & P. Sabino, 2015. "Enhancing Least Squares Monte Carlo with diffusion bridges: an application to energy facilities," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 761-772, May.
    4. 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.
    5. Jan Baldeaux & Eckhard Platen, 2012. "Computing Functionals of Multidimensional Diffusions via Monte Carlo Methods," Papers 1204.1126, arXiv.org.

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