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On the primal-dual algorithm for callable Bermudan options

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  • Maximilian Mair
  • Jan Maruhn

Abstract

This paper discusses various extensions and implementation aspects of the primal-dual algorithm of Andersen and Broadie for the pricing of Bermudan options. The main emphasis is on a generalization of the dual lower and upper bounds to the case of mixed buyer and seller exercise, along with a detailed analysis of the sharpness of the bounds. As it turns out, the method as well as the convergence analysis can even be extended to conditional exercise rights and autotrigger strategies. These theoretical results are accompanied by a detailed description of the algorithmic implementation, including a robust regression method and the choice of suitable basis functions. Detailed numerical examples show that the algorithm leads to surprisingly tight bounds even for the case of high-dimensional callable Bermudan pricing problems. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Maximilian Mair & Jan Maruhn, 2013. "On the primal-dual algorithm for callable Bermudan options," Review of Derivatives Research, Springer, vol. 16(1), pages 79-110, April.
    • Handle: RePEc:kap:revdev:v:16:y:2013:i:1:p:79-110
    DOI: 10.1007/s11147-012-9078-9
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    References listed on IDEAS

    as
    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.
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    5. Pizzi Claudio & Pellizzari Paolo, 2002. "Monte Carlo Pricing of American Options Using Nonparametric Regression," Finance 0207007, University Library of Munich, Germany, revised 04 Mar 2003.
    6. 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.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. Mark Broadie & Menghui Cao, 2008. "Improved lower and upper bound algorithms for pricing American options by simulation," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 845-861.
    9. 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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    More about this item

    Keywords

    Bermudan options; Dual bounds; Mixed exercise; G13;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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