Pricing High-Dimensional American Options Using Local Consistency Conditions

S.J. Berridge, J.M. Schumacher

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherFinance
Number of pages33
Volume2004-19
Publication statusPublished - 2004

Publication series

NameCentER Discussion Paper
Volume2004-19

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Sampling
Linear programming
Markov processes
Costs

Keywords

  • option pricing
  • inequality
  • markov chains

Cite this

Berridge, S. J., & Schumacher, J. M. (2004). Pricing High-Dimensional American Options Using Local Consistency Conditions. (CentER Discussion Paper; Vol. 2004-19). Tilburg: Finance.
Berridge, S.J. ; Schumacher, J.M. / Pricing High-Dimensional American Options Using Local Consistency Conditions. Tilburg : Finance, 2004. (CentER Discussion Paper).
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Berridge, SJ & Schumacher, JM 2004 'Pricing High-Dimensional American Options Using Local Consistency Conditions' CentER Discussion Paper, vol. 2004-19, Finance, Tilburg.

Pricing High-Dimensional American Options Using Local Consistency Conditions. / Berridge, S.J.; Schumacher, J.M.

Tilburg : Finance, 2004. (CentER Discussion Paper; Vol. 2004-19).

Research output: Working paperDiscussion paperOther research output

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N2 - 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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KW - inequality

KW - markov chains

M3 - Discussion paper

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Berridge SJ, Schumacher JM. Pricing High-Dimensional American Options Using Local Consistency Conditions. Tilburg: Finance. 2004. (CentER Discussion Paper).