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Practical policy iteration: Generic methods for obtaining rapid and tight bounds for Bermudan exotic derivatives using Monte Carlo simulation

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  • Beveridge, Christopher
  • Joshi, Mark
  • Tang, Robert

Abstract

We introduce a set of improvements which allow the calculation of very tight lower bounds for Bermudan derivatives using Monte Carlo simulation. These tight lower bounds can be computed quickly, and with minimal hand-crafting. Our focus is on accelerating policy iteration to the point where it can be used in similar computation times to the basic least-squares approach, but in doing so introduce a number of improvements which can be applied to both the least-squares approach and the calculation of upper bounds using the Andersen–Broadie method. The enhancements to the least-squares method improve both accuracy and efficiency.

Suggested Citation

  • Beveridge, Christopher & Joshi, Mark & Tang, Robert, 2013. "Practical policy iteration: Generic methods for obtaining rapid and tight bounds for Bermudan exotic derivatives using Monte Carlo simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1342-1361.
    • Handle: RePEc:eee:dyncon:v:37:y:2013:i:7:p:1342-1361
    DOI: 10.1016/j.jedc.2013.03.004
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    References listed on IDEAS

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    11. 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.
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    Citations

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    Cited by:

    1. Christopher Beveridge & Mark Joshi, 2011. "Monte Carlo Bounds for Game Options Including Convertible Bonds," Management Science, INFORMS, vol. 57(5), pages 960-974, May.
    2. Maciej Klimek & Marcin Pitera, 2014. "The least squares method for option pricing revisited," Papers 1404.7438, arXiv.org, revised Nov 2015.
    3. Mark Joshi & Oh Kang Kwon, 2016. "Least Squares Monte Carlo Credit Value Adjustment With Small And Unidirectional Bias," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-16, December.
    4. 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.
    5. Nicholas Andrew Yap Swee Guan, 2015. "Regression and Convex Switching System Methods for Stochastic Control Problems with Applications to Multiple-Exercise Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5-2015, January-A.
    6. Joshi, Mark & Tang, Robert, 2014. "Effective sub-simulation-free upper bounds for the Monte Carlo pricing of callable derivatives and various improvements to existing methodologies," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 25-45.
    7. Jeechul Woo & Chenru Liu & Jaehyuk Choi, 2024. "Leave‐one‐out least squares Monte Carlo algorithm for pricing Bermudan options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(8), pages 1404-1428, August.
    8. Christopher Beveridge & Mark Joshi, 2014. "The Efficient Computation Of Prices And Greeks For Callable Range Accruals Using The Displaced-Diffusion Lmm," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 1-47.
    9. David A. Goldberg & Yilun Chen, 2018. "Polynomial time algorithm for optimal stopping with fixed accuracy," Papers 1807.02227, arXiv.org, revised May 2024.
    10. Mark S. Joshi, 2016. "Analysing the bias in the primal-dual upper bound method for early exercisable derivatives: bounds, estimation and removal," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 519-533, April.
    11. Nicholas Andrew Yap Swee Guan, 2015. "Regression and Convex Switching System Methods for Stochastic Control Problems with Applications to Multiple-Exercise Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 26, July-Dece.

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    More about this item

    Keywords

    Bermudan option; LIBOR market model; Early exercise; Monte Carlo;
    All these keywords.

    JEL classification:

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

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