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The optimal method for pricing Bermudan options by simulation

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  • Alfredo Ibáñez
  • Carlos Velasco

Abstract

Least‐squares methods enable us to price Bermudan‐style options by Monte Carlo simulation. They are based on estimating the option continuation value by least‐squares. We show that the Bermudan price is maximized when this continuation value is estimated near the exercise boundary, which is equivalent to implicitly estimating the optimal exercise boundary by using the value‐matching condition. Localization is the key difference with respect to global regression methods, but is fundamental for optimal exercise decisions and requires estimation of the continuation value by iterating local least‐squares (because we estimate and localize the exercise boundary at the same time). In the numerical example, in agreement with this optimality, the new prices or lower bounds (i) improve upon the prices reported by other methods and (ii) are very close to the associated dual upper bounds. We also study the method's convergence.

Suggested Citation

  • Alfredo Ibáñez & Carlos Velasco, 2018. "The optimal method for pricing Bermudan options by simulation," Mathematical Finance, Wiley Blackwell, vol. 28(4), pages 1143-1180, October.
    • Handle: RePEc:bla:mathfi:v:28:y:2018:i:4:p:1143-1180
    DOI: 10.1111/mafi.12158
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    Cited by:

    1. Huang, Min & Luo, Guo, 2022. "A simple and efficient numerical method for pricing discretely monitored early-exercise options," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    2. Min Huang & Guo Luo, 2019. "A simple and efficient numerical method for pricing discretely monitored early-exercise options," Papers 1905.13407, arXiv.org, revised Jun 2019.

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