IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v16y2016i5p763-776.html
   My bibliography  Save this article

Optimal hedging in an extended binomial market under transaction costs

Author

Listed:
  • Norman Josephy
  • Lucia Kimball
  • Victoria Steblovskaya

Abstract

We develop an approach to optimal hedging of a contingent claim under proportional transaction costs in a discrete time financial market model which extends the binomial market model with transaction costs. Our model relaxes the binomial assumption on the stock price ratios to the case where the stock price ratio distribution has bounded support. Non-self-financing hedging strategies are studied to construct an optimal hedge for an investor who takes a short position in a European contingent claim settled by delivery. We develop the theoretical basis for our optimal hedging approach, extending results obtained in our previous work. Specifically, we derive a no-arbitrage option price interval and establish properties of the non-self-financing strategies and their residuals. Based on the theoretical foundation, we develop a computational algorithm for optimizing an investor relevant criterion over the set of admissible non-self-financing hedging strategies. We demonstrate the applicability of our approach using both simulated data and real market data.

Suggested Citation

  • Norman Josephy & Lucia Kimball & Victoria Steblovskaya, 2016. "Optimal hedging in an extended binomial market under transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 16(5), pages 763-776, May.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:5:p:763-776
    DOI: 10.1080/14697688.2015.1039225
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697688.2015.1039225
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697688.2015.1039225?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. Boyle, Phelim P & Vorst, Ton, 1992. "Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, vol. 47(1), pages 271-293, March.
    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. Norman Josephy & Lucia Kimball & Victoria Steblovskaya, 2017. "On The Numerical Aspects Of Optimal Option Hedging With Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-22, February.

    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. Jay Cao & Jacky Chen & John Hull & Zissis Poulos, 2021. "Deep Hedging of Derivatives Using Reinforcement Learning," Papers 2103.16409, arXiv.org.
    2. Wang, Jun & Liang, Jin-Rong & Lv, Long-Jin & Qiu, Wei-Yuan & Ren, Fu-Yao, 2012. "Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 750-759.
    3. Luca Di Persio & Luca Prezioso & Kai Wallbaum, 2019. "Closed-End Formula for options linked to Target Volatility Strategies," Papers 1902.08821, arXiv.org.
    4. Zachary Feinstein & Birgit Rudloff, 2018. "Scalar multivariate risk measures with a single eligible asset," Papers 1807.10694, arXiv.org, revised Feb 2021.
    5. Dichtl, Hubert & Drobetz, Wolfgang, 2011. "Portfolio insurance and prospect theory investors: Popularity and optimal design of capital protected financial products," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1683-1697, July.
    6. Peter Christoffersen & Ruslan Goyenko & Kris Jacobs & Mehdi Karoui, 2018. "Illiquidity Premia in the Equity Options Market," Review of Financial Studies, Society for Financial Studies, vol. 31(3), pages 811-851.
    7. Melino, Angelo & Turnbull, Stuart M., 1995. "Misspecification and the pricing and hedging of long-term foreign currency options," Journal of International Money and Finance, Elsevier, vol. 14(3), pages 373-393, June.
    8. Huh, Sahn-Wook & Lin, Hao & Mello, Antonio S., 2015. "Options market makers׳ hedging and informed trading: Theory and evidence," Journal of Financial Markets, Elsevier, vol. 23(C), pages 26-58.
    9. Lin, Zih-Ying & Chang, Chuang-Chang & Wang, Yaw-Huei, 2018. "The impacts of asymmetric information and short sales on the illiquidity risk premium in the stock option market," Journal of Banking & Finance, Elsevier, vol. 94(C), pages 152-165.
    10. Bas Peeters & Cees L. Dert & André Lucas, 2003. "Black Scholes for Portfolios of Options in Discrete Time: the Price is Right, the Hedge is wrong," Tinbergen Institute Discussion Papers 03-090/2, Tinbergen Institute.
    11. Al–Zhour, Zeyad & Barfeie, Mahdiar & Soleymani, Fazlollah & Tohidi, Emran, 2019. "A computational method to price with transaction costs under the nonlinear Black–Scholes model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 291-301.
    12. Kanne, Stefan & Korn, Olaf & Uhrig-Homburg, Marliese, 2023. "Stock illiquidity and option returns," Journal of Financial Markets, Elsevier, vol. 63(C).
    13. Baule, Rainer & Münchhalfen, Patrick & Shkel, David & Tallau, Christian, 2023. "Fair-washing in the market for structured retail products? Voluntary self-regulation versus government regulation," Journal of Banking & Finance, Elsevier, vol. 148(C).
    14. Reiß, Ariane, 1997. "Option replication with large transactions costs," Tübinger Diskussionsbeiträge 106, University of Tübingen, School of Business and Economics.
    15. Fleten, Stein-Erik & Lindset, Snorre, 2008. "Optimal hedging strategies for multi-period guarantees in the presence of transaction costs: A stochastic programming approach," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1680-1689, March.
    16. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    17. Lin, Zhongguo & Han, Liyan & Li, Wei, 2021. "Option replication with transaction cost under Knightian uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    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. Jouini, Elyes, 2000. "Price functionals with bid-ask spreads: an axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 547-558, December.
    20. N. Chidambaran, 2007. "Density estimation through quasi-analytic Monte-Carlo simulation: Options arbitrage with transactions costs," Review of Quantitative Finance and Accounting, Springer, vol. 28(1), pages 101-122, January.

    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:taf:quantf:v:16:y:2016:i:5:p:763-776. 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 Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.