IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01069270.html
   My bibliography  Save this paper

A backward dual representation for the quantile hedging of Bermudan options

Author

Listed:
  • 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] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - 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
    as

    Download full text from publisher

    File URL: https://hal.science/hal-01069270v2/document
    Download Restriction: no
    ---><---

    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. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    5. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
    6. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    7. Ying Jiao & Olivier Klopfenstein & Peter Tankov, 2013. "Hedging under multiple risk constraints," Papers 1309.5094, arXiv.org.
    8. 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.
    9. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    10. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    11. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    12. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
    13. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2016. "Hedging under an expected loss constraint with small transaction costs," Post-Print hal-00863562, HAL.
    2. 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.
    3. Adrien Nguyen Huu & Nadia Oudjane, 2014. "Hedging Expected Losses on Derivatives in Electricity Futures Markets," Papers 1401.8271, arXiv.org.
    4. Bruno Bouchard & Ngoc-Minh Dang, 2013. "Generalized stochastic target problems for pricing and partial hedging under loss constraints—application in optimal book liquidation," Finance and Stochastics, Springer, vol. 17(1), pages 31-72, January.
    5. Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2013. "Hedging under an expected loss constraint with small transaction costs," Papers 1309.4916, arXiv.org, revised Sep 2014.
    6. Yuk-Loong Chow & Xiang Yu & Chao Zhou, 2020. "On Dynamic Programming Principle for Stochastic Control Under Expectation Constraints," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 803-818, June.
    7. Cambier, Adrien & Chardy, Matthieu & Figueiredo, Rosa & Ouorou, Adam & Poss, Michael, 2022. "Optimizing subscriber migrations for a telecommunication operator in uncertain context," European Journal of Operational Research, Elsevier, vol. 298(1), pages 308-321.
    8. Libura, Marek, 2007. "On the adjustment problem for linear programs," European Journal of Operational Research, Elsevier, vol. 183(1), pages 125-134, November.
    9. Christophe Loussouarn & Carine Franc & Yann Videau & Julien Mousquès, 2021. "Can General Practitioners Be More Productive? The Impact of Teamwork and Cooperation with Nurses on GP Activities," Health Economics, John Wiley & Sons, Ltd., vol. 30(3), pages 680-698, March.
    10. Tschakert, Petra, 2016. "Shifting Discourses of Vilification and the Taming of Unruly Mining Landscapes in Ghana," World Development, Elsevier, vol. 86(C), pages 123-132.
    11. Isabelle Boutron & Peter John & David J. Torgerson, 2010. "Reporting Methodological Items in Randomized Experiments in Political Science," The ANNALS of the American Academy of Political and Social Science, , vol. 628(1), pages 112-131, March.
    12. Ben Slimane, Faten & Padilla Angulo, Laura, 2019. "Strategic change and corporate governance: Evidence from the stock exchange industry," Journal of Business Research, Elsevier, vol. 103(C), pages 206-218.
    13. Weijun Xie & Yanfeng Ouyang & Sze Chun Wong, 2016. "Reliable Location-Routing Design Under Probabilistic Facility Disruptions," Transportation Science, INFORMS, vol. 50(3), pages 1128-1138, August.
    14. Natalia Nikolaevna Natocheeva* & Yuri Alexandrovich Rovensky & Yuri Yuryevich Rusanov & Tatiana Viktorovna Belyanchikova & Anna Anatolevna Staurskaya, 2018. "Optimizing Variability of Approaches to Regulatory Financing of Higher Education Services," The Journal of Social Sciences Research, Academic Research Publishing Group, pages 221-227:3.
    15. Sahar Validi & Arijit Bhattacharya & P. J. Byrne, 2020. "Sustainable distribution system design: a two-phase DoE-guided meta-heuristic solution approach for a three-echelon bi-objective AHP-integrated location-routing model," Annals of Operations Research, Springer, vol. 290(1), pages 191-222, July.
    16. Andy Hall, 2005. "Capacity development for agricultural biotechnology in developing countries: an innovation systems view of what it is and how to develop it," Journal of International Development, John Wiley & Sons, Ltd., vol. 17(5), pages 611-630.
    17. Athinoula A. Kosti & Simon Colreavy-Donnelly & Fabio Caraffini & Zacharias A. Anastassi, 2020. "Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    18. Bruno Frey, 2005. "Problems with Publishing: Existing State and Solutions," European Journal of Law and Economics, Springer, vol. 19(2), pages 173-190, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-01069270. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.