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Adaptive (Quasi-)Monte Carlo Methods for Pricing Path-Dependent Options

In: Monte Carlo and Quasi-Monte Carlo Methods 2008

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  • Roman N. Makarov

    (Wilfrid Laurier University, Department of Mathematics)

Abstract

We study a recently developed adaptive path-integration technique for pricing financial derivatives. The method is based on the rearrangement and splitting of path-integral variables to apply a combination of bridge sampling, adaptive methods of numerical integration, and the quasi-Monte Carlo method. We study the subregion adaptive Vegas-type method Suave from the Cuba library and propose a new variance reduction method with a multivariate piecewise constant sampling density. Two models of asset pricing are considered: the constant elasticity of variance diffusion model and the variance gamma Lévy model. Numerical tests are done for Asian-type options.

Suggested Citation

  • Roman N. Makarov, 2009. "Adaptive (Quasi-)Monte Carlo Methods for Pricing Path-Dependent Options," Springer Books, in: Pierre L' Ecuyer & Art B. Owen (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2008, pages 529-544, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-04107-5_34
    DOI: 10.1007/978-3-642-04107-5_34
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