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Upper Bounds for Bermudan Style Derivatives

Author

Listed:
  • Kolodko A.

    (Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin and Institute of Computational Mathematics and Mathematical Geophysics, Prosp. Lavrentjeva 6, 630090 Novosibirsk, Russia; E-mail: . Supported by the DFG Research Center “Mathematics for key technologies” (FZT 86) in Berlin. kolodko@wias-berlin.de)

  • Schoenmakers J.

    (Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin; E-mail: schoenma@wias-berlin.de)

Abstract

Based on a duality approach for Monte Carlo construction of upper bounds for American/Bermudan derivatives (Rogers, Haugh & Kogan), we present a new algorithm for computing dual upper bounds in a more efficient way. The method is applied to Bermudan swaptions in the context of a LIBOR market model, where the dual upper bound is constructed from the maximum of still alive swaptions. We give a numerical comparison with Andersen's lower bound method.

Suggested Citation

  • Kolodko A. & Schoenmakers J., 2004. "Upper Bounds for Bermudan Style Derivatives," Monte Carlo Methods and Applications, De Gruyter, vol. 10(3-4), pages 331-343, December.
    • Handle: RePEc:bpj:mcmeap:v:10:y:2004:i:3-4:p:331-343:n:15
    DOI: 10.1515/mcma.2004.10.3-4.331
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    Citations

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    Cited by:

    1. John Schoenmakers, 2012. "A pure martingale dual for multiple stopping," Finance and Stochastics, Springer, vol. 16(2), pages 319-334, April.
    2. Louis Bhim & Reiichiro Kawai, 2018. "Smooth Upper Bounds For The Price Function Of American Style Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-38, February.
    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. Jérôme Lelong, 2016. "Dual pricing of American options by Wiener chaos expansion," Working Papers hal-01299819, HAL.
    5. Jin, Xing & Yang, Cheng-Yu, 2016. "Efficient estimation of lower and upper bounds for pricing higher-dimensional American arithmetic average options by approximating their payoff functions," International Review of Financial Analysis, Elsevier, vol. 44(C), pages 65-77.
    6. 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.
    7. 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.
    8. John Schoenmakers & Junbo Huang & Jianing Zhang, 2011. "Optimal dual martingales, their analysis and application to new algorithms for Bermudan products," Papers 1111.6038, arXiv.org, revised Feb 2012.
    9. Christian Bender & Anastasia Kolodko & John Schoenmakers, 2008. "Enhanced policy iteration for American options via scenario selection," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 135-146.
    10. Jérôme Lelong, 2018. "Dual pricing of American options by Wiener chaos expansion," Post-Print hal-01299819, HAL.
    11. J'er^ome Lelong, 2016. "Pricing American options using martingale bases," Papers 1604.03317, arXiv.org.

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