Quasi-Monte Carlo methods for the Heston model
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2012
- DOI:
- 10.48550/arXiv.1202.3217
- arXiv:
- arXiv:1202.3217
- Bibcode:
- 2012arXiv1202.3217B
- Keywords:
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- Quantitative Finance - Computational Finance
- E-Print:
- 20 pages. Submitted