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Pricing high-dimensional Americal options using local consistency conditions

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Author Info
Berridge, S.J.
Schumacher, J.M. (Tilburg University, Center for Economic Research)

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Abstract

We investigate a new method for pricing high-dimensional American options. The method is of finite difference type but is also related to Monte Carlo techniques in that it involves a representative sampling of the underlying variables. An approximating Markov chain is built using this sampling and linear programming is used to satisfy local consistency conditions at each point related to the infinitesimal generator or transition density. The algorithm for constructing the matrix can be parallelised easily; moreover once it has been obtained it can be reused to generate quick solutions for a large class of related problems. We provide pricing results for geometric average options in up to ten dimensions, and compare these with accurate benchmarks.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 19.

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Date of creation: 2004
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Handle: RePEc:dgr:kubcen:200419

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Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques

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  1. Berridge, S.J. & Schumacher, J.M., 2002. "An irregular grid approach for pricing high-dimensional American options," Discussion Paper 99, Tilburg University, Center for Economic Research. [Downloadable!]
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  2. Barraquand, J?r?me & Martineau, Didier, 1995. "Numerical Valuation of High Dimensional Multivariate American Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(03), pages 383-405, September. [Downloadable!]
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