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Pricing Bermudan options by nonparametric regression: optimal rates of convergence for lower estimates

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  • Denis Belomestny

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  • Denis Belomestny, 2011. "Pricing Bermudan options by nonparametric regression: optimal rates of convergence for lower estimates," Finance and Stochastics, Springer, vol. 15(4), pages 655-683, December.
    • Handle: RePEc:spr:finsto:v:15:y:2011:i:4:p:655-683
    DOI: 10.1007/s00780-010-0132-x
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    References listed on IDEAS

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    1. 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.
    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. Denis Belomestny & Grigori Milstein & Vladimir Spokoiny, 2009. "Regression methods in pricing American and Bermudan options using consumption processes," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 315-327.
    4. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    5. repec:hum:wpaper:sfb649dp2006-051 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Aleksandar Arandjelovi'c & Pavel V. Shevchenko & Tomoko Matsui & Daisuke Murakami & Tor A. Myrvoll, 2024. "Solving stochastic climate-economy models: A deep least-squares Monte Carlo approach," Papers 2408.09642, arXiv.org.
    2. Fabian Dickmann & Nikolaus Schweizer, 2014. "Faster Comparison of Stopping Times by Nested Conditional Monte Carlo," Papers 1402.0243, arXiv.org.
    3. Pascal Létourneau & Lars Stentoft, 2019. "Bootstrapping the Early Exercise Boundary in the Least-Squares Monte Carlo Method," JRFM, MDPI, vol. 12(4), pages 1-21, December.
    4. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen & Timo Welti, 2019. "Solving high-dimensional optimal stopping problems using deep learning," Papers 1908.01602, arXiv.org, revised Aug 2021.
    5. Bünyamin Erkan & Jean-Luc Prigent, 2020. "About Long-Term Cross-Currency Bermuda Swaption Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 56(1), pages 239-262, June.
    6. Ruimeng Hu, 2019. "Deep Learning for Ranking Response Surfaces with Applications to Optimal Stopping Problems," Papers 1901.03478, arXiv.org, revised Mar 2020.
    7. Fabozzi, Frank J. & Paletta, Tommaso & Tunaru, Radu, 2017. "An improved least squares Monte Carlo valuation method based on heteroscedasticity," European Journal of Operational Research, Elsevier, vol. 263(2), pages 698-706.
    8. David A. Goldberg & Yilun Chen, 2018. "Polynomial time algorithm for optimal stopping with fixed accuracy," Papers 1807.02227, arXiv.org, revised May 2024.
    9. Li, Chenxu & Ye, Yongxin, 2019. "Pricing and Exercising American Options: an Asymptotic Expansion Approach," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    10. Yi Yang & Jianan Wang & Youhua Chen & Zhiyuan Chen & Yanchu Liu, 2020. "Optimal procurement strategies for contractual assembly systems with fluctuating procurement price," Annals of Operations Research, Springer, vol. 291(1), pages 1027-1059, August.
    11. Zhiyi Shen & Chengguo Weng, 2019. "A Backward Simulation Method for Stochastic Optimal Control Problems," Papers 1901.06715, arXiv.org.
    12. Daniel Z. Zanger, 2020. "General Error Estimates for the Longstaff–Schwartz Least-Squares Monte Carlo Algorithm," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 923-946, August.
    13. Denis Belomestny & Fabian Dickmann & Tigran Nagapetyan, 2013. "Pricing American options via multi-level approximation methods," Papers 1303.1334, arXiv.org, revised Dec 2013.
    14. Christian Yeo, 2023. "An analysis of least squares regression and neural networks approximation for the pricing of swing options," Papers 2307.04510, arXiv.org.
    15. Denis Belomestny & John Schoenmakers & Vladimir Spokoiny & Bakhyt Zharkynbay, 2018. "Optimal stopping via reinforced regression," Papers 1808.02341, arXiv.org, revised Jul 2019.
    16. 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.
    17. Mike Ludkovski, 2020. "mlOSP: Towards a Unified Implementation of Regression Monte Carlo Algorithms," Papers 2012.00729, arXiv.org, revised Oct 2022.
    18. 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.
    19. Nan Chen & Yanchu Liu, 2014. "American Option Sensitivities Estimation via a Generalized Infinitesimal Perturbation Analysis Approach," Operations Research, INFORMS, vol. 62(3), pages 616-632, June.
    20. Denis Belomestny & John Schoenmakers & Fabian Dickmann, 2013. "Multilevel dual approach for pricing American style derivatives," Finance and Stochastics, Springer, vol. 17(4), pages 717-742, October.

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    More about this item

    Keywords

    Bermudan options; Nonparametric regression; Boundary condition; Suboptimal stopping rules; 62G08; 65C05; 60G40; G10; G12; G13;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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