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An Irregular Grid Approach for Pricing High-Dimensional American Options

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  • Berridge, S.J.
  • Schumacher, J.M.

    (Tilburg University, Center for Economic Research)

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 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.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2004-18.

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Date of creation: 2004
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Handle: RePEc:dgr:kubcen:200418

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Web page: http://center.uvt.nl

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Keywords: option pricing; inequality; markov chains;

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  1. Boyle, Phelim P & Evnine, Jeremy & Gibbs, Stephen, 1989. "Numerical Evaluation of Multivariate Contingent Claims," Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 241-50.
  2. Evans, Michael & Swartz, Timothy, 2000. "Approximating Integrals via Monte Carlo and Deterministic Methods," OUP Catalogue, Oxford University Press, number 9780198502784.
  3. Barraquand, Jérôme & 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.
  4. Manuel Moreno & Javier R. Navas, 2001. "On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives," Economics Working Papers 543, Department of Economics and Business, Universitat Pompeu Fabra.
  5. Lars Stentoft, 2004. "Assessing the Least Squares Monte-Carlo Approach to American Option Valuation," Review of Derivatives Research, Springer, vol. 7(2), pages 129-168, 08.
  6. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-47.
  7. M. A. H. Dempster & J. P. Hutton, 1999. "Pricing American Stock Options by Linear Programming," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 229-254.
  8. Boyle, Phelim P. & Kolkiewicz, Adam W. & Tan, Ken Seng, 2003. "An improved simulation method for pricing high-dimensional American derivatives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(3), pages 315-322.
  9. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
  10. Philip Protter & Emmanuelle Clément & Damien Lamberton, 2002. "An analysis of a least squares regression method for American option pricing," Finance and Stochastics, Springer, vol. 6(4), pages 449-471.
  11. Lars Stentoft, 2004. "Convergence of the Least Squares Monte Carlo Approach to American Option Valuation," Management Science, INFORMS, vol. 50(9), pages 1193-1203, September.
  12. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
  13. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
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Cited by:
  1. Berridge, S.J. & Schumacher, J.M., 2004. "Pricing High-Dimensional American Options Using Local Consistency Conditions," Discussion Paper 2004-19, Tilburg University, Center for Economic Research.
  2. Berridge, S.J. & Schumacher, J.M., 2004. "Using Localised Quadratic Functions on an Irregular Grid for Pricing High-Dimensional American Options," Discussion Paper 2004-20, Tilburg University, Center for Economic Research.

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