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Upper bounds for Bermudan options on Markovian data using nonparametric regression and a reduced number of nested Monte Carlo steps

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  • Kohler Michael

    (Technische Universit¨at Darmstadt, Fachbereich Mathematik, Darmstadt, Deutschland)

  • Krzyzak Adam
  • Walk Harro

    (Universität Stuttgart, Institute of Stochastics and Applications, Stuttgart, Deutschland)

Abstract

This paper is concerned with evaluation of American options in discrete time, also called Bermudan options. We use the dual approach to derive upper bounds on the price of such options using only a reduced number of nested Monte Carlo steps. The key idea is to apply nonparametric regression to estimate continuation values and all other required conditional expectations and to combine the resulting estimate with another estimate computed by using only a reduced number of nested Monte Carlo steps. The expectation of the resulting estimate is an upper bound on the option price. It is shown that the estimates of the option prices are universally consistent, i.e., they converge to the true price regardless of the structure of the continuation values. The finite sample behavior is validated by experiments on simulated data.

Suggested Citation

  • Kohler Michael & Krzyzak Adam & Walk Harro, 2009. "Upper bounds for Bermudan options on Markovian data using nonparametric regression and a reduced number of nested Monte Carlo steps," Statistics & Risk Modeling, De Gruyter, vol. 26(4), pages 275-288, July.
    • Handle: RePEc:bpj:strimo:v:26:y:2009:i:4:p:275-288:n:3
    DOI: 10.1524/stnd.2008.1014
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    References listed on IDEAS

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    1. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    2. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    3. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    4. Nan Chen & Paul Glasserman, 2007. "Additive and multiplicative duals for American option pricing," Finance and Stochastics, Springer, vol. 11(2), pages 153-179, April.
    5. Denis Belomestny & Christian Bender & John Schoenmakers, 2009. "True Upper Bounds For Bermudan Products Via Non‐Nested Monte Carlo," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 53-71, January.
    6. 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.
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