IDEAS home Printed from https://ideas.repec.org/b/spr/mathfi/v17y2023i4d10.1007_s11579-023-00345-9.html
   My bibliography  Save this book

On intermediate marginals in martingale optimal transportation

Author

Listed:
  • Julian Sester

    (National University of Singapore)

Abstract

We study the influence of additional intermediate marginal distributions on the value of the martingale optimal transport problem. From a financial point of view, this corresponds to taking into account call option prices not only, as usual, for those call options where the respective future maturities coincide with the maturities of some exotic derivative but also additional maturities and then to study the effect on model-independent price bounds for the exotic derivative. We characterize market settings, i.e., combinations of the payoff of exotic derivatives, call option prices and marginal distributions that guarantee improved price bounds as well as those market settings that exclude any improvement. Eventually, we showcase in numerous examples that the consideration of additional price information on vanilla options may have a considerable impact on the resultant model-independent price bounds.

Suggested Citation

  • Julian Sester, 2023. "On intermediate marginals in martingale optimal transportation," Mathematics and Financial Economics, Springer, volume 17, number 2, February.
    • Handle: RePEc:spr:mathfi:v:17:y:2023:i:4:d:10.1007_s11579-023-00345-9
    DOI: 10.1007/s11579-023-00345-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11579-023-00345-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11579-023-00345-9?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Marcel Nutz & Johannes Wiesel & Long Zhao, 2022. "Limits of Semistatic Trading Strategies," Papers 2204.12251, arXiv.org.
    2. Thibaut Lux & Antonis Papapantoleon, 2016. "Improved Fr\'echet$-$Hoeffding bounds on $d$-copulas and applications in model-free finance," Papers 1602.08894, arXiv.org, revised Jun 2017.
    3. Gaoyue Guo & Jan Obloj, 2017. "Computational Methods for Martingale Optimal Transport problems," Papers 1710.07911, arXiv.org, revised Apr 2019.
    4. 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.
    5. David Hobson & Dominykas Norgilas, 2019. "Robust bounds for the American put," Finance and Stochastics, Springer, vol. 23(2), pages 359-395, April.
    6. Mathias Beiglbock & Benjamin Jourdain & William Margheriti & Gudmund Pammer, 2021. "Stability of the Weak Martingale Optimal Transport Problem," Papers 2109.06322, arXiv.org, revised Apr 2022.
    7. Cousot, Laurent, 2007. "Conditions on option prices for absence of arbitrage and exact calibration," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3377-3397, November.
    8. Acciaio, Beatrice & Larsson, Martin & Schachermayer, Walter, 2017. "The space of outcomes of semi-static trading strategies need not be closed," LSE Research Online Documents on Economics 69804, London School of Economics and Political Science, LSE Library.
    9. David Hobson & Martin Klimmek, 2015. "Robust price bounds for the forward starting straddle," Finance and Stochastics, Springer, vol. 19(1), pages 189-214, January.
    10. Mathias Beiglbock & Pierre Henry-Labord`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929, arXiv.org, revised Feb 2013.
    11. Beatrice Acciaio & Martin Larsson & Walter Schachermayer, 2017. "The space of outcomes of semi-static trading strategies need not be closed," Finance and Stochastics, Springer, vol. 21(3), pages 741-751, July.
    12. J. T. Chang & D. Pollard, 1997. "Conditioning as disintegration," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 51(3), pages 287-317, November.
    13. Stephan Eckstein & Michael Kupper, 2019. "Martingale transport with homogeneous stock movements," Papers 1908.10242, arXiv.org, revised May 2021.
    14. Matteo Burzoni, 2015. "Arbitrage and Hedging in model-independent markets with frictions," Papers 1512.01488, arXiv.org, revised Aug 2016.
    15. Ariel Neufeld & Julian Sester, 2021. "On the stability of the martingale optimal transport problem: A set-valued map approach," Papers 2102.02718, arXiv.org, revised Apr 2021.
    16. Marcel Nutz & Florian Stebegg & Xiaowei Tan, 2017. "Multiperiod Martingale Transport," Papers 1703.10588, arXiv.org, revised May 2019.
    17. B. Acciaio & M. Beiglböck & F. Penkner & W. Schachermayer, 2016. "A Model-Free Version Of The Fundamental Theorem Of Asset Pricing And The Super-Replication Theorem," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 233-251, April.
    18. Neufeld, Ariel & Sester, Julian, 2021. "On the stability of the martingale optimal transport problem: A set-valued map approach," Statistics & Probability Letters, Elsevier, vol. 176(C).
    19. 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.
    20. Ariel Neufeld & Julian Sester, 2021. "Model-free price bounds under dynamic option trading," Papers 2101.01024, arXiv.org, revised Jul 2021.
    21. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2020. "Pathwise superhedging on prediction sets," Finance and Stochastics, Springer, vol. 24(1), pages 215-248, January.
    22. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2020. "Detecting and repairing arbitrage in traded option prices," Papers 2008.09454, arXiv.org.
    23. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2020. "Detecting and Repairing Arbitrage in Traded Option Prices," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(5), pages 345-373, September.
    24. Patrick Cheridito & Michael Kupper & Ludovic Tangpi, 2016. "Duality formulas for robust pricing and hedging in discrete time," Papers 1602.06177, arXiv.org, revised Sep 2017.
    25. Peter Tankov, 2010. "Improved Frechet bounds and model-free pricing of multi-asset options," Papers 1004.4153, arXiv.org, revised Mar 2011.
    26. Nicole Bäuerle & Daniel Schmithals, 2021. "Consistent Upper Price Bounds For Exotic Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 1-29, March.
    27. Pierre Henry-Labordère, 2013. "Automated Option Pricing: Numerical Methods," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(08), pages 1-27.
    28. 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.
    29. Luca De Gennaro Aquino & Carole Bernard, 2019. "Bounds on Multi-asset Derivatives via Neural Networks," Papers 1911.05523, arXiv.org, revised Nov 2020.
    30. Luca De Gennaro Aquino & Carole Bernard, 2020. "Bounds On Multi-Asset Derivatives Via Neural Networks," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(08), pages 1-31, December.
    31. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2020. "Model-free bounds for multi-asset options using option-implied information and their exact computation," Papers 2006.14288, arXiv.org, revised Jan 2022.
    32. Stephan Eckstein & Michael Kupper, 2021. "Martingale transport with homogeneous stock movements," Quantitative Finance, Taylor & Francis Journals, vol. 21(2), pages 271-280, February.
    33. Julian Sester, 2020. "Robust Bounds For Derivative Prices In Markovian Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(03), pages 1-39, May.
    34. Zhaoxu Hou & Jan Obłój, 2018. "Robust pricing–hedging dualities in continuous time," Finance and Stochastics, Springer, vol. 22(3), pages 511-567, July.
    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. Julian Sester, 2023. "On intermediate Marginals in Martingale Optimal Transportation," Papers 2307.09710, arXiv.org, revised Nov 2023.
    2. Jonathan Ansari & Eva Lütkebohmert & Ariel Neufeld & Julian Sester, 2024. "Improved robust price bounds for multi-asset derivatives under market-implied dependence information," Finance and Stochastics, Springer, vol. 28(4), pages 911-964, October.
    3. Jonathan Ansari & Eva Lutkebohmert & Ariel Neufeld & Julian Sester, 2022. "Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information," Papers 2204.01071, arXiv.org, revised Sep 2023.
    4. Ariel Neufeld & Julian Sester, 2021. "A deep learning approach to data-driven model-free pricing and to martingale optimal transport," Papers 2103.11435, arXiv.org, revised Dec 2022.
    5. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2023. "Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation," Management Science, INFORMS, vol. 69(4), pages 2051-2068, April.
    6. Alessandro Doldi & Marco Frittelli & Emanuela Rosazza Gianin, 2024. "On entropy martingale optimal transport theory," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 1-42, June.
    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. Ariel Neufeld & Julian Sester, 2021. "Model-free price bounds under dynamic option trading," Papers 2101.01024, arXiv.org, revised Jul 2021.
    9. Alessandro Doldi & Marco Frittelli, 2023. "Entropy martingale optimal transport and nonlinear pricing–hedging duality," Finance and Stochastics, Springer, vol. 27(2), pages 255-304, April.
    10. Sester, Julian, 2024. "A multi-marginal c-convex duality theorem for martingale optimal transport," Statistics & Probability Letters, Elsevier, vol. 210(C).
    11. Marcel Nutz & Johannes Wiesel & Long Zhao, 2022. "Martingale Schr\"odinger Bridges and Optimal Semistatic Portfolios," Papers 2204.12250, arXiv.org.
    12. Linn Engstrom & Sigrid Kallblad & Johan Karlsson, 2024. "Computation of Robust Option Prices via Structured Multi-Marginal Martingale Optimal Transport," Papers 2406.09959, arXiv.org, revised Mar 2025.
    13. Benjamin Jourdain & Gilles Pagès, 2022. "Convex Order, Quantization and Monotone Approximations of ARCH Models," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2480-2517, December.
    14. Ariel Neufeld & Julian Sester & Daiying Yin, 2022. "Detecting data-driven robust statistical arbitrage strategies with deep neural networks," Papers 2203.03179, arXiv.org, revised Feb 2024.
    15. Marcel Nutz & Johannes Wiesel & Long Zhao, 2023. "Martingale Schrödinger bridges and optimal semistatic portfolios," Finance and Stochastics, Springer, vol. 27(1), pages 233-254, January.
    16. Neufeld, Ariel & Sester, Julian, 2021. "On the stability of the martingale optimal transport problem: A set-valued map approach," Statistics & Probability Letters, Elsevier, vol. 176(C).
    17. Marcel Nutz & Florian Stebegg, 2016. "Canonical Supermartingale Couplings," Papers 1609.02867, arXiv.org, revised Nov 2017.
    18. Stephan Eckstein & Michael Kupper, 2018. "Computation of optimal transport and related hedging problems via penalization and neural networks," Papers 1802.08539, arXiv.org, revised Jan 2019.
    19. Nicole Bäuerle & Daniel Schmithals, 2019. "Martingale optimal transport in the discrete case via simple linear programming techniques," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(3), pages 453-476, December.
    20. Ariel Neufeld & Julian Sester, 2023. "Neural networks can detect model-free static arbitrage strategies," Papers 2306.16422, arXiv.org, revised Aug 2024.

    More about this item

    Keywords

    Martingale optimal transport; Additional information; Robust price bounds; Intermediate marginals;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    Statistics

    Access and download statistics

    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:spr:mathfi:v:17:y:2023:i:4:d:10.1007_s11579-023-00345-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.