IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v30y2020i3p833-868.html
   My bibliography  Save this article

Hedging nontradable risks with transaction costs and price impact

Author

Listed:
  • Álvaro Cartea
  • Ryan Donnelly
  • Sebastian Jaimungal

Abstract

A risk‐averse agent hedges her exposure to a nontradable risk factor U using a correlated traded asset S and accounts for the impact of her trades on both factors. The effect of the agent's trades on U is referred to as cross‐impact. By solving the agent's stochastic control problem, we obtain a closed‐form expression for the optimal strategy when the agent holds a linear position in U. When the exposure to the nontradable risk factor ψ(UT) is nonlinear, we provide an approximation to the optimal strategy in closed‐form, and prove that the value function is correctly approximated by this strategy when cross‐impact and risk‐aversion are small. We further prove that when ψ(UT) is nonlinear, the approximate optimal strategy can be written in terms of the optimal strategy for a linear exposure with the size of the position changing dynamically according to the exposure's “Delta” under a particular probability measure.

Suggested Citation

  • Álvaro Cartea & Ryan Donnelly & Sebastian Jaimungal, 2020. "Hedging nontradable risks with transaction costs and price impact," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 833-868, July.
    • Handle: RePEc:bla:mathfi:v:30:y:2020:i:3:p:833-868
    DOI: 10.1111/mafi.12259
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/mafi.12259
    Download Restriction: no
    File URL: https://libkey.io/10.1111/mafi.12259?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. M. R. Grasselli, 2011. "Getting Real with Real Options: A Utility–Based Approach for Finite–Time Investment in Incomplete Markets," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 38(5-6), pages 740-764, June.
    2. Rama Cont & Arseniy Kukanov & Sasha Stoikov, 2014. "The Price Impact of Order Book Events," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 47-88.
    3. Tim Leung & Matthew Lorig, 2016. "Optimal static quadratic hedging," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1341-1355, September.
    4. Grasselli, Matheus & Henderson, Vicky, 2009. "Risk aversion and block exercise of executive stock options," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 109-127, January.
    5. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373, October.
    6. Tim Leung & Ronnie Sircar, 2009. "Accounting For Risk Aversion, Vesting, Job Termination Risk And Multiple Exercises In Valuation Of Employee Stock Options," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 99-128, January.
    7. Potters, Marc & Bouchaud, Jean-Philippe, 2003. "More statistical properties of order books and price impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 133-140.
    8. Álvaro Cartea & Sebastian Jaimungal, 2017. "Irreversible Investments And Ambiguity Aversion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-26, November.
    9. J. Donier & J. Bonart & I. Mastromatteo & J.-P. Bouchaud, 2015. "A fully consistent, minimal model for non-linear market impact," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1109-1121, July.
    10. Jonathan Donier & Julius Bonart & Iacopo Mastromatteo & Jean-Philippe Bouchaud, 2014. "A fully consistent, minimal model for non-linear market impact," Papers 1412.0141, arXiv.org, revised Mar 2015.
    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. Alvaro Cartea & Ryan Donnelly & Sebastian Jaimungal, 2019. "Hedging Non-Tradable Risks with Transaction Costs and Price Impact," Papers 1908.00054, arXiv.org, revised Mar 2020.
    2. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    3. Fengpei Li & Vitalii Ihnatiuk & Ryan Kinnear & Anderson Schneider & Yuriy Nevmyvaka, 2022. "Do price trajectory data increase the efficiency of market impact estimation?," Papers 2205.13423, arXiv.org, revised Mar 2023.
    4. Emilio Said, 2022. "Market Impact: Empirical Evidence, Theory and Practice," Working Papers hal-03668669, HAL.
    5. Ke Xu & Martin D. Gould & Sam D. Howison, 2019. "Multi-Level Order-Flow Imbalance in a Limit Order Book," Papers 1907.06230, arXiv.org, revised Oct 2019.
    6. Matthew Dicks & Andrew Paskaramoorthy & Tim Gebbie, 2023. "Many learning agents interacting with an agent-based market model," Papers 2303.07393, arXiv.org, revised Aug 2024.
    7. Fabrizio Lillo, 2021. "Order flow and price formation," Papers 2105.00521, arXiv.org.
    8. Marvin S. Mueller, 2016. "A stochastic Stefan-type problem under first-order boundary conditions," Papers 1601.03968, arXiv.org, revised Oct 2018.
    9. Emilio Said, 2022. "Market Impact: Empirical Evidence, Theory and Practice," Papers 2205.07385, arXiv.org.
    10. M. Derksen & B. Kleijn & R. de Vilder, 2019. "Clearing price distributions in call auctions," Papers 1904.07583, arXiv.org, revised Nov 2019.
    11. Johannes Gerer & Gregor Dorfleitner, 2016. "A Note On Utility Indifference Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-17, September.
    12. Damian Eduardo Taranto & Giacomo Bormetti & Jean-Philippe Bouchaud & Fabrizio Lillo & Bence Toth, 2016. "Linear models for the impact of order flow on prices I. Propagators: Transient vs. History Dependent Impact," Papers 1602.02735, arXiv.org.
    13. Fr'ed'eric Bucci & Michael Benzaquen & Fabrizio Lillo & Jean-Philippe Bouchaud, 2019. "Slow decay of impact in equity markets: insights from the ANcerno database," Papers 1901.05332, arXiv.org, revised Jan 2019.
    14. Fr'ed'eric Bucci & Iacopo Mastromatteo & Michael Benzaquen & Jean-Philippe Bouchaud, 2019. "Impact is not just volatility," Papers 1905.04569, arXiv.org.
    15. Francesco Cordoni & Fabrizio Lillo, 2022. "Transient impact from the Nash equilibrium of a permanent market impact game," Papers 2205.00494, arXiv.org, revised Mar 2023.
    16. Louis Saddier & Matteo Marsili, 2023. "A Bayesian theory of market impact," Papers 2303.08867, arXiv.org, revised May 2024.
    17. Frédéric Bucci & Michael Benzaquen & Fabrizio Lillo & Jean-Philippe Bouchaud, 2019. "Slow Decay of Impact in Equity Markets: Insights from the ANcerno Database," Post-Print hal-02323357, HAL.
    18. Eduardo Dávila & Daniel Graves & Cecilia Parlatore, 2024. "The Value of Arbitrage," Journal of Political Economy, University of Chicago Press, vol. 132(6), pages 1947-1993.
    19. Mohammed Salek & Damien Challet & Ioane Muni Toke, 2023. "Price impact in equity auctions: zero, then linear," Working Papers hal-03938660, HAL.
    20. Salma Elomari-Kessab & Guillaume Maitrier & Julius Bonart & Jean-Philippe Bouchaud, 2024. ""Microstructure Modes" -- Disentangling the Joint Dynamics of Prices & Order Flow," Papers 2405.10654, arXiv.org.

    More about this item

    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:bla:mathfi:v:30:y:2020:i:3:p:833-868. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    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.