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An Irregular Grid Approach for Pricing High-Dimensional American Options

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Listed:
  • Berridge, S.J.

    (Tilburg University, Center For Economic Research)

  • 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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Suggested Citation

  • Berridge, S.J. & Schumacher, J.M., 2004. "An Irregular Grid Approach for Pricing High-Dimensional American Options," Discussion Paper 2004-18, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:7371422b-c2a8-4b71-8749-686be8bdd86a
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    References listed on IDEAS

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    1. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    2. 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 241-250.
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    4. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    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, August.
    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 113-147.
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    10. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
    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. 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.
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    Cited by:

    1. Vladislav Kargin, 2005. "Lattice Option Pricing By Multidimensional Interpolation," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 635-647, October.
    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.
    3. Berridge, S.J. & Schumacher, J.M., 2004. "Pricing High-Dimensional American Options Using Local Consistency Conditions," Other publications TiSEM 8c8de631-5039-4eec-a965-3, Tilburg University, School of Economics and Management.

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    More about this item

    Keywords

    option pricing; inequality; markov chains;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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