IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v20y2017i01ns0219024917500029.html
   My bibliography  Save this article

On The Numerical Aspects Of Optimal Option Hedging With Transaction Costs

Author

Listed:
  • NORMAN JOSEPHY

    (Department of Mathematical Sciences, Bentley University, 175 Forest Street, Waltham, MA 02452-4705, USA)

  • LUCIA KIMBALL

    (Department of Mathematical Sciences, Bentley University, 175 Forest Street, Waltham, MA 02452-4705, USA)

  • VICTORIA STEBLOVSKAYA

    (Department of Mathematical Sciences, Bentley University, 175 Forest Street, Waltham, MA 02452-4705, USA)

Abstract

We present a numerical study of non-self-financing hedging of European options under proportional transaction costs. We describe an algorithmic approach based on a discrete time financial market model that extends the classical binomial model. We review the analytical basis for our algorithm and present a variety of empirical results using real market data. The performance of the algorithm is evaluated by comparing to a Black–Scholes delta hedge with transaction costs incorporated. We also evaluate the impact of recalibrating the hedging strategy one or more times during the life of the option using the most recent market data. These results are compared to a recalibrated Black–Scholes delta hedge modified for transaction costs.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:01:n:s0219024917500029
    DOI: 10.1142/S0219024917500029
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024917500029
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024917500029?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. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    2. 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.
    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. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    2. Luca Di Persio & Luca Prezioso & Kai Wallbaum, 2019. "Closed-End Formula for options linked to Target Volatility Strategies," Papers 1902.08821, arXiv.org.
    3. Mastinšek Miklavž, 2015. "Reduction of the Mean Hedging Transaction Costs / Redukcija povprečnih transakcijskih stroškov hedging tehnike," Naše gospodarstvo/Our economy, Sciendo, vol. 61(5), pages 23-31, October.
    4. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    5. Pascal Franc{c}ois & Genevi`eve Gauthier & Fr'ed'eric Godin & Carlos Octavio P'erez Mendoza, 2024. "Enhancing Deep Hedging of Options with Implied Volatility Surface Feedback Information," Papers 2407.21138, arXiv.org.
    6. Wang, Xiao-Tian & Wu, Min & Zhou, Ze-Min & Jing, Wei-Shu, 2012. "Pricing European option with transaction costs under the fractional long memory stochastic volatility model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1469-1480.
    7. Emmanuel Denis & Yuri Kabanov, 2010. "Mean square error for the Leland–Lott hedging strategy: convex pay-offs," Finance and Stochastics, Springer, vol. 14(4), pages 625-667, December.
    8. Yuan, Xianghui & Li, Xiang, 2022. "Delta-hedging demand and intraday momentum: Evidence from China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    9. Raquel M. Gaspar & Paulo M. Silva, 2023. "Investors’ perspective on portfolio insurance," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 22(1), pages 49-79, January.
    10. 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.
    11. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    12. 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.
    13. Koichi Matsumoto, 2007. "Portfolio Insurance with Liquidity Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(4), pages 363-386, December.
    14. Kanne, Stefan & Korn, Olaf & Uhrig-Homburg, Marliese, 2023. "Stock illiquidity and option returns," Journal of Financial Markets, Elsevier, vol. 63(C).
    15. Siu, Tak Kuen, 2023. "European option pricing with market frictions, regime switches and model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 233-250.
    16. Wang, Xiao-Tian & Zhu, En-Hui & Tang, Ming-Ming & Yan, Hai-Gang, 2010. "Scaling and long-range dependence in option pricing II: Pricing European option with transaction costs under the mixed Brownian–fractional Brownian model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 445-451.
    17. Hu, Yuan & Lindquist, W. Brent & Rachev, Svetlozar T. & Shirvani, Abootaleb & Fabozzi, Frank J., 2022. "Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    18. Borochin, Paul & Wu, Zekun & Zhao, Yanhui, 2021. "The effect of option-implied skewness on delta- and vega-hedged option returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 74(C).
    19. Chamorro, Jose M. & Perez de Villarreal, Jose M., 2000. "Mutual fund evaluation: a portfolio insurance approach: A heuristic application in Spain," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 83-104, August.
    20. repec:dau:papers:123456789/4654 is not listed on IDEAS
    21. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.

    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:wsi:ijtafx:v:20:y:2017:i:01:n:s0219024917500029. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.