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Pricing high-dimensional Bermudan options with hierarchical tensor formats

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  • Christian Bayer
  • Martin Eigel
  • Leon Sallandt
  • Philipp Trunschke

Abstract

An efficient compression technique based on hierarchical tensors for popular option pricing methods is presented. It is shown that the "curse of dimensionality" can be alleviated for the computation of Bermudan option prices with the Monte Carlo least-squares approach as well as the dual martingale method, both using high-dimensional tensorized polynomial expansions. This discretization allows for a simple and computationally cheap evaluation of conditional expectations. Complexity estimates are provided as well as a description of the optimization procedures in the tensor train format. Numerical experiments illustrate the favourable accuracy of the proposed methods. The dynamical programming method yields results comparable to recent Neural Network based methods.

Suggested Citation

  • Christian Bayer & Martin Eigel & Leon Sallandt & Philipp Trunschke, 2021. "Pricing high-dimensional Bermudan options with hierarchical tensor formats," Papers 2103.01934, arXiv.org, revised Mar 2021.
    • Handle: RePEc:arx:papers:2103.01934
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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. Mike Ludkovski, 2020. "mlOSP: Towards a Unified Implementation of Regression Monte Carlo Algorithms," Papers 2012.00729, arXiv.org, revised Oct 2022.
    4. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    5. Jérôme Lelong, 2018. "Dual pricing of American options by Wiener chaos expansion," Post-Print hal-01299819, HAL.
    6. Jérôme Lelong, 2019. "Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach," Working Papers hal-01983115, HAL.
    7. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    8. 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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