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

Roman N. Makarov ()
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Roman N. Makarov: Wilfrid Laurier University, Department of Mathematics

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2008, 2009, pp 529-544 from Springer

Abstract: 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.

Keywords: Probability Density Function; Variance Reduction; Variance Gamma; Gamma Process; Inverse Cumulative Distribution Function (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04107-5_34

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DOI: 10.1007/978-3-642-04107-5_34

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