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A backward dual representation for the quantile hedging of Bermudan options

Author

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  • Bruno Bouchard

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Jean-François Chassagneux

    (Imperial College London)

  • Géraldine Bouveret

    (Imperial College London)

Abstract

Within a Markovian complete financial market, we consider the problem of hedging a Bermudan option with a given probability. Using stochastic target and duality arguments, we derive a backward numerical scheme for the Fenchel transform of the pricing function. This algorithm is similar to the usual American backward induction, except that it requires two additional Fenchel transformations at each exercise date. We provide numerical illustrations.

Suggested Citation

  • Bruno Bouchard & Jean-François Chassagneux & Géraldine Bouveret, 2016. "A backward dual representation for the quantile hedging of Bermudan options," Post-Print hal-01069270, HAL.
    • Handle: RePEc:hal:journl:hal-01069270
    Note: View the original document on HAL open archive server: https://hal.science/hal-01069270v2
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    References listed on IDEAS

    as
    1. Bruno Bouchard & Thanh Nam Vu, 2012. "A Stochastic Target Approach for P&L Matching Problems," Mathematics of Operations Research, INFORMS, vol. 37(3), pages 526-558, August.
    2. Bally, Vlad & Pagès, Gilles, 2003. "Error analysis of the optimal quantization algorithm for obstacle problems," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 1-40, July.
    3. repec:dau:papers:123456789/4273 is not listed on IDEAS
    4. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
    5. Ying Jiao & Olivier Klopfenstein & Peter Tankov, 2013. "Hedging under multiple risk constraints," Papers 1309.5094, arXiv.org.
    6. Vlad Bally & Gilles Pagès & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 119-168, January.
    7. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
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    Cited by:

    1. Dumitrescu, Roxana & Elie, Romuald & Sabbagh, Wissal & Zhou, Chao, 2023. "A new Mertens decomposition of Yg,ξ-submartingale systems. Application to BSDEs with weak constraints at stopping times," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 183-205.
    2. Géraldine Bouveret, 2018. "Portfolio Optimization Under A Quantile Hedging Constraint," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-36, November.
    3. Cyril B'en'ezet & Jean-Franc{c}ois Chassagneux & Mohan Yang, 2023. "An optimal transport approach for the multiple quantile hedging problem," Papers 2308.01121, arXiv.org.
    4. Géraldine Bouveret & Athena Picarelli, 2020. "A Level-Set Approach for Stochastic Optimal Control Problems Under Controlled-Loss Constraints," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 779-805, September.
    5. Cyril B'en'ezet & Jean-Franc{c}ois Chassagneux & Christoph Reisinger, 2019. "A numerical scheme for the quantile hedging problem," Papers 1902.11228, arXiv.org.
    6. Roxana Dumitrescu & Romuald Elie & Wissal Sabbagh & Chao Zhou, 2017. "A new Mertens decomposition of $\mathscr{Y}^{g,\xi}$-submartingale systems. Application to BSDEs with weak constraints at stopping times," Papers 1708.05957, arXiv.org, revised May 2023.

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