An Improved Algorithm for Pricing Derivatives Using Sobol Quasirandom Sequences
17 Pages Posted: 21 Aug 2012
Date Written: August 21, 2012
It is often argued that Quasi-Monte Carlo Methods (QMC ) only work for problems of low effective dimension that encompass most of financial problems. We will show here some evidence that, with the Sobol construction, they can be suited for problems with high effective dimension in the truncation sense as well as (moderately) high effective dimension in the superposition sense. We propose a methodology for obtaining the initial direction integers that are a central piece for generation of "good" Sobol sequences and show several examples both financial and nonfinancial where they can be used. Our sequences can deal with up to 35,000-dimensional problems.
Keywords: Sobol sequences, quasi-Monte Carlo methods, numerical integration, derivatives pricing
JEL Classification: G13, C63, G32
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