An irregular grid approach for pricing high-dimensional American options

We propose and test a new method for pricing American options in a high-dimensional setting. The method is centered around the approximation of the associated complementarity problem on an irregular grid. We approximate the partial differential operator on this grid by appealing to the SDE represent...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2008-12, Vol.222 (1), p.94-111
Main Authors: Berridge, S.J., Schumacher, J.M.
Format: Article
Language:English
Subjects:
American options
Exact sciences and technology
Free boundary problems
High-dimensional problems
Markov chain approximation
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods
Numerical methods in probability and statistics
Operator theory
Optimal stopping
Ordinary differential equations
Partial differential equations
Sciences and techniques of general use
Unstructured mesh
Variational inequalities
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Summary:We propose and test a new method for pricing American options in a high-dimensional setting. The method is centered around the approximation of the associated complementarity problem on an irregular grid. We approximate the partial differential operator on this grid by appealing to the SDE representation of the underlying process and computing the root of the transition probability matrix of an approximating Markov chain. Experimental results in five-dimensions are presented for four different payoff functions.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2007.10.045