IDEAS home Printed from https://ideas.repec.org/a/kap/apfinm/v27y2020i1d10.1007_s10690-019-09283-3.html
   My bibliography  Save this article

Hedging Derivatives on Two Assets with Model Risk

Author

Listed:
  • Koichi Matsumoto

    (Kyushu University)

  • Keita Shimizu

    (Kyushu University)

Abstract

This paper studies a static hedging problem of derivatives when the model risk exists. When the payoff of derivative depends on one asset, Matsumoto (Int J Financ Eng 4(4):1750042, 2017b) solves the problem. We extend his result to derivatives on two assets. Though the optimal solution is more complicated, we show that the problem can be solved numerically in an algebraic way. Further we give some simple numerical examples to show our method works well.

Suggested Citation

  • Koichi Matsumoto & Keita Shimizu, 2020. "Hedging Derivatives on Two Assets with Model Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 27(1), pages 83-95, March.
    • Handle: RePEc:kap:apfinm:v:27:y:2020:i:1:d:10.1007_s10690-019-09283-3
    DOI: 10.1007/s10690-019-09283-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10690-019-09283-3
    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/s10690-019-09283-3?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. Martin Schweizer, 1995. "Variance-Optimal Hedging in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 1-32, February.
    2. Ales Cerny, 2004. "Dynamic programming and mean-variance hedging in discrete time," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(1), pages 1-25.
    3. Koichi Matsumoto, 2009. "Mean-Variance Hedging with Uncertain Trade Execution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 219-252.
    4. R. Tevzadze & T. Uzunashvili, 2012. "Robust Mean-Variance Hedging And Pricing Of Contingent Claims In A One Period Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-9.
    5. T. J. Lyons, 1995. "Uncertain volatility and the risk-free synthesis of derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 117-133.
    6. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    7. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "Hedging Derivative Securities and Incomplete Markets: An (epsilon)-Arbitrage Approach," Operations Research, INFORMS, vol. 49(3), pages 372-397, June.
    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. Augustyniak, Maciej & Godin, Frédéric & Simard, Clarence, 2019. "A profitable modification to global quadratic hedging," Journal of Economic Dynamics and Control, Elsevier, vol. 104(C), pages 111-131.
    2. Antoine Jacquier & Patrick Roome, 2015. "Black-Scholes in a CEV random environment," Papers 1503.08082, arXiv.org, revised Nov 2017.
    3. Li, Xinpeng & Peng, Shige, 2011. "Stopping times and related Itô's calculus with G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1492-1508, July.
    4. Kim Weston, 2016. "Stability of utility maximization in nonequivalent markets," Finance and Stochastics, Springer, vol. 20(2), pages 511-541, April.
    5. Elyes Jouini & Pierre-Francois Koehl, "undated". "Pricing of Non-redundant Derivatives in a Complete Market," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-009, New York University, Leonard N. Stern School of Business-.
    6. Chen An & Mahayni Antje B., 2008. "Endowment Assurance Products: Effectiveness of Risk-Minimizing Strategies under Model Risk," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 2(2), pages 1-29, March.
    7. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
    8. Daniel Bartl & Michael Kupper & David J. Prömel & Ludovic Tangpi, 2019. "Duality for pathwise superhedging in continuous time," Finance and Stochastics, Springer, vol. 23(3), pages 697-728, July.
    9. Alexandre Carbonneau & Fr'ed'eric Godin, 2021. "Deep equal risk pricing of financial derivatives with non-translation invariant risk measures," Papers 2107.11340, arXiv.org.
    10. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2018. "Robust XVA," Papers 1808.04908, arXiv.org, revised Feb 2020.
    11. Park, Kyunghyun & Wong, Hoi Ying & Yan, Tingjin, 2023. "Robust retirement and life insurance with inflation risk and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 1-30.
    12. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    13. Secomandi, Nicola, 2022. "Quadratic hedging of risk neutral values," Energy Economics, Elsevier, vol. 112(C).
    14. Sergey Nadtochiy & Jan Obłój, 2017. "Robust Trading Of Implied Skew," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-41, March.
    15. Julian Holzermann, 2019. "Term Structure Modeling under Volatility Uncertainty," Papers 1904.02930, arXiv.org, revised Sep 2021.
    16. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2020. "Pathwise superhedging on prediction sets," Finance and Stochastics, Springer, vol. 24(1), pages 215-248, January.
    17. Dirk Becherer & Klebert Kentia, 2017. "Good Deal Hedging and Valuation under Combined Uncertainty about Drift and Volatility," Papers 1704.02505, arXiv.org.
    18. Gondzio, Jacek & Kouwenberg, Roy & Vorst, Ton, 2003. "Hedging options under transaction costs and stochastic volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1045-1068, April.
    19. Rosella Castellano & Roy Cerqueti, 2013. "Roots and effects of financial misperception in a stochastic dominance framework," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(6), pages 3371-3389, October.
    20. Jean-Pierre Fouque & Ning Ning, 2017. "Uncertain Volatility Models with Stochastic Bounds," Papers 1702.05036, arXiv.org.

    More about this item

    Keywords

    Hedging; Derivatives; Model risk;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:kap:apfinm:v:27:y:2020:i:1:d:10.1007_s10690-019-09283-3. 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.