IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v63y2017i7p2323-2339.html
   My bibliography  Save this article

Superreplication of Financial Derivatives via Convex Programming

Author

Listed:
  • Nabil Kahalé

    (ESCP Europe and LabEx RéFi, 75011 Paris, France)

Abstract

We give a method based on convex programming to calculate the optimal superreplicating and subreplicating prices and corresponding hedging portfolios of a financial derivative in terms of other financial derivatives in a discrete-time setting. Our method produces a model that matches the superreplicating (or subreplicating) price within an arbitrary precision and is consistent with the other financial derivatives prices. Applications include robust replication in terms of call prices with various strikes and maturities of forward start options, volatility and variance swaps and derivatives, cliquet calls, barrier options, and lookback and Asian options. Numerical examples show that, in some cases, the best superreplicating and/or subreplicating prices are within 10% of the price obtained by a standard model but considerably differ from it in other cases. Our method can incorporate bid-ask spreads, interest rates and dividends, and various limitations to the diffusion model.

Suggested Citation

  • Nabil Kahalé, 2017. "Superreplication of Financial Derivatives via Convex Programming," Management Science, INFORMS, vol. 63(7), pages 2323-2339, July.
    • Handle: RePEc:inm:ormnsc:v:63:y:2017:i:7:p:2323-2339
    DOI: 10.1287/mnsc.2017.2786
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/mnsc.2017.2786
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.2017.2786?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Mark Britten‐Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, April.
    2. Laurence, Peter & Wang, Tai-Ho, 2009. "Sharp distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 35-47, February.
    3. Peter Carr & Roger Lee & Liuren Wu, 2012. "Variance swaps on time-changed Lévy processes," Finance and Stochastics, Springer, vol. 16(2), pages 335-355, April.
    4. L. Carassus & E. Gobet & E. Temam, 2007. "A Class of Financial Products and Models Where Super-replication Prices are Explicit," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 4, pages 67-84, World Scientific Publishing Co. Pte. Ltd..
    5. Pierre Henry-Labordère & Nizar Touzi, 2016. "An explicit martingale version of the one-dimensional Brenier theorem," Finance and Stochastics, Springer, vol. 20(3), pages 635-668, July.
    6. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    7. A. Galichon & P. Henry-Labord`ere & N. Touzi, 2014. "A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options," Papers 1401.3921, arXiv.org.
    8. Pierre Henry-Labord`ere & Jan Ob{l}'oj & Peter Spoida & Nizar Touzi, 2012. "The maximum maximum of a martingale with given $n$ marginals," Papers 1203.6877, arXiv.org, revised Jan 2016.
    9. Mark Broadie & Ashish Jain, 2008. "The Effect Of Jumps And Discrete Sampling On Volatility And Variance Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(08), pages 761-797.
    10. Dimitris Bertsimas & Ioana Popescu, 2002. "On the Relation Between Option and Stock Prices: A Convex Optimization Approach," Operations Research, INFORMS, vol. 50(2), pages 358-374, April.
    11. David Hobson & Martin Klimmek, 2015. "Robust price bounds for the forward starting straddle," Finance and Stochastics, Springer, vol. 19(1), pages 189-214, January.
    12. Simon, S. & Goovaerts, M. J. & Dhaene, J., 2000. "An easy computable upper bound for the price of an arithmetic Asian option," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 175-183, May.
    13. Mark H. A. Davis & David G. Hobson, 2007. "The Range Of Traded Option Prices," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 1-14, January.
    14. Peter Laurence & Tai-Ho Wang, 2005. "Sharp Upper and Lower Bounds for Basket Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(3), pages 253-282.
    15. David Hobson & Martin Klimmek, 2012. "Model-independent hedging strategies for variance swaps," Finance and Stochastics, Springer, vol. 16(4), pages 611-649, October.
    16. H. Albrecher & P. A. Mayer & W. Schoutens, 2008. "General Lower Bounds for Arithmetic Asian Option Prices," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 123-149.
    17. Jun-ya Gotoh & Hiroshi Konno, 2002. "Bounding Option Prices by Semidefinite Programming: A Cutting Plane Algorithm," Management Science, INFORMS, vol. 48(5), pages 665-678, May.
    18. Alexander M. G. Cox & Jiajie Wang, 2011. "Root's barrier: Construction, optimality and applications to variance options," Papers 1104.3583, arXiv.org, revised Mar 2013.
    19. Peter Laurence & Tai-Ho Wang, 2008. "Distribution-free upper bounds for spread options and market-implied antimonotonicity gap," The European Journal of Finance, Taylor & Francis Journals, vol. 14(8), pages 717-734.
    20. J. Frederic Bonnans & Xiaolu Tan, 2013. "A model-free no-arbitrage price bound for variance options," Post-Print inria-00634387, HAL.
    21. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
    Full references (including those not matched with items on IDEAS)

    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. Henry-Labordère, Pierre & Tan, Xiaolu & Touzi, Nizar, 2016. "An explicit martingale version of the one-dimensional Brenier’s Theorem with full marginals constraint," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2800-2834.
    2. Pierre Henry-Labordère & Nizar Touzi, 2016. "An explicit martingale version of the one-dimensional Brenier theorem," Finance and Stochastics, Springer, vol. 20(3), pages 635-668, July.
    3. Gaoyue Guo & Jan Obloj, 2017. "Computational Methods for Martingale Optimal Transport problems," Papers 1710.07911, arXiv.org, revised Apr 2019.
    4. Mathias Beiglbock & Marcel Nutz & Florian Stebegg, 2019. "Fine Properties of the Optimal Skorokhod Embedding Problem," Papers 1903.03887, arXiv.org, revised Apr 2020.
    5. Nicole Bauerle & Daniel Schmithals, 2019. "Consistent upper price bounds for exotic options given a finite number of call prices and their convergence," Papers 1907.09144, arXiv.org.
    6. Mathias Beiglböck & Pierre Henry-Labordère & Friedrich Penkner, 2013. "Model-independent bounds for option prices—a mass transport approach," Finance and Stochastics, Springer, vol. 17(3), pages 477-501, July.
    7. Sergey Badikov & Mark H. A. Davis & Antoine Jacquier, 2018. "Perturbation analysis of sub/super hedging problems," Papers 1806.03543, arXiv.org, revised May 2021.
    8. Tavin, Bertrand, 2015. "Detection of arbitrage in a market with multi-asset derivatives and known risk-neutral marginals," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 158-178.
    9. Marcel Nutz & Florian Stebegg, 2016. "Canonical Supermartingale Couplings," Papers 1609.02867, arXiv.org, revised Nov 2017.
    10. Marcel Nutz & Florian Stebegg & Xiaowei Tan, 2017. "Multiperiod Martingale Transport," Papers 1703.10588, arXiv.org, revised May 2019.
    11. Hansjörg Albrecher & Philipp Mayer, 2010. "Semi-Static Hedging Strategies For Exotic Options," World Scientific Book Chapters, in: Rüdiger Kiesel & Matthias Scherer & Rudi Zagst (ed.), Alternative Investments And Strategies, chapter 14, pages 345-373, World Scientific Publishing Co. Pte. Ltd..
    12. David Hobson & Dominykas Norgilas, 2019. "Robust bounds for the American put," Finance and Stochastics, Springer, vol. 23(2), pages 359-395, April.
    13. Erhan Bayraktar & Shuoqing Deng & Dominykas Norgilas, 2023. "Supermartingale Brenier’s Theorem with Full-Marginal Constraint," World Scientific Book Chapters, in: Robert A Jarrow & Dilip B Madan (ed.), Peter Carr Gedenkschrift Research Advances in Mathematical Finance, chapter 17, pages 569-636, World Scientific Publishing Co. Pte. Ltd..
    14. David Hobson & Martin Klimmek, 2015. "Robust price bounds for the forward starting straddle," Finance and Stochastics, Springer, vol. 19(1), pages 189-214, January.
    15. Alexander M. G. Cox & Annemarie M. Grass, 2023. "Robust option pricing with volatility term structure -- An empirical study for variance options," Papers 2312.09201, arXiv.org.
    16. Mathias Beiglboeck & Alexander Cox & Martin Huesmann, 2017. "The geometry of multi-marginal Skorokhod Embedding," Papers 1705.09505, arXiv.org.
    17. Y. Dolinsky & H. M. Soner, 2014. "Martingale optimal transport in the Skorokhod space," Papers 1404.1516, arXiv.org, revised Feb 2015.
    18. Nutz, Marcel & Stebegg, Florian & Tan, Xiaowei, 2020. "Multiperiod martingale transport," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1568-1615.
    19. Peña, Javier & Vera, Juan C. & Zuluaga, Luis F., 2012. "Computing arbitrage upper bounds on basket options in the presence of bid–ask spreads," European Journal of Operational Research, Elsevier, vol. 222(2), pages 369-376.
    20. Guo, Gaoyue & Tan, Xiaolu & Touzi, Nizar, 2017. "Tightness and duality of martingale transport on the Skorokhod space," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 927-956.

    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:inm:ormnsc:v:63:y:2017:i:7:p:2323-2339. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.