An irregular grid method for high-dimensional free-boundary problems in finance

Authors:
Steffan Berridge;J. M. Schumacher
Affiliations:
Department of Econometrics and Operations Research and Center for Economic Research (CentER), Tilburg University, Postbus 90153, 5000 LE Tilburg, The Netherlands;Department of Econometrics and Operations Research and Center for Economic Research (CentER), Tilburg University, Postbus 90153, 5000 LE Tilburg, The Netherlands
Venue:
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Year:
2004

Citing 6
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Convergence of the Least Squares Monte Carlo Approach to American Option Valuation

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Regression methods for pricing complex American-style options

IEEE Transactions on Neural Networks

An irregular grid approach for pricing high-dimensional American options

Journal of Computational and Applied Mathematics

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Abstract

We propose and test a new method for pricing American options in a high-dimensional setting. The method is centred around the approximation of the associated variational inequality on an irregular grid. We approximate the effect of the partial differential operator on this grid by appealing to the stochastic differential equation (SDE) representation of the stock process and computing a root of the transition probability matrix of an approximating Markov chain. The results of numerical tests in five dimensions are promising.