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Recursive lower and dual upper bounds for Bermudan-style options

Author

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  • Ibáñez, Alfredo
  • Velasco, Carlos
Abstract
Although Bermudan options are routinely priced by simulation and least-squares methods using lower and dual upper bounds, the latter are hardly optimized. In this paper, we optimize recursive upper bounds, which are more tractable than the original/nonrecursive ones, and derive two new results: (1) An upper bound based on (a martingale that depends on) stopping times is independent of the next-stage exercise decision and hence cannot be optimized. Instead, we optimize the recursive lower bound, and use its optimal recursive policy to evaluate the upper bound as well. (2) Less time-intensive upper bounds that are based on a continuation-value function only need this function in the continuation region, where this continuation value is less nonlinear and easier to fit (than in the entire support). In the numerical exercise, both upper bounds improve over state-of-the-art methods (including standard least-squares and pathwise optimization). Specifically, the very small gap between the lower and the upper bounds derived in (1) implies the recursive policy and the associated martingale are near optimal, so that these two specific lower/upper bounds are hard to improve, yet the upper bound is tighter than the lower bound.

Suggested Citation

  • Ibáñez, Alfredo & Velasco, Carlos, 2020. "Recursive lower and dual upper bounds for Bermudan-style options," European Journal of Operational Research, Elsevier, vol. 280(2), pages 730-740.
    • Handle: RePEc:eee:ejores:v:280:y:2020:i:2:p:730-740
    DOI: 10.1016/j.ejor.2019.07.031
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    Cited by:

    1. Anna Kamille Nyegaard & Johan Raunkjær Ott & Mogens Steffensen, 2021. "An Intrinsic Value Approach to Valuation with Forward–Backward Loops in Dividend Paying Stocks," Mathematics, MDPI, vol. 9(13), pages 1-23, June.
    2. Wei, Wei & Zhu, Dan, 2022. "Generic improvements to least squares monte carlo methods with applications to optimal stopping problems," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1132-1144.

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