IDEAS home Printed from https://ideas.repec.org/a/eee/finlet/v62y2024ipas1544612324001314.html
   My bibliography  Save this article

Relationship between deep hedging and delta hedging: Leveraging a statistical arbitrage strategy

Author

Listed:
  • Horikawa, Hiroaki
  • Nakagawa, Kei

Abstract

In this study, we explore the links between deep hedging and delta hedging using a statistical arbitrage strategy. Specifically, we show that hedging that minimizes loss risk combines delta hedging with a statistical arbitrage strategy. The numerical experiments in a simple Black–Scholes world also verify these results. Moreover, it is known that the existence of statistical arbitrages can hamper proper learning of deep hedging. For this problem, the obtained relationship and analysis of the profit and loss (PnL) distribution of deep hedging provide us with insight into risk measures that are resistant to statistical arbitrages. We conclude that the use of these robust risk measures allows us to ignore the estimation of drift terms in asset price processes.

Suggested Citation

  • Horikawa, Hiroaki & Nakagawa, Kei, 2024. "Relationship between deep hedging and delta hedging: Leveraging a statistical arbitrage strategy," Finance Research Letters, Elsevier, vol. 62(PA).
    • Handle: RePEc:eee:finlet:v:62:y:2024:i:pa:s1544612324001314
    DOI: 10.1016/j.frl.2024.105101
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1544612324001314
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.frl.2024.105101?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. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
    2. R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, January.
    3. Carbonneau, Alexandre, 2021. "Deep hedging of long-term financial derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 327-340.
    4. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    5. Alexandre Carbonneau & Fr'ed'eric Godin, 2021. "Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments," Papers 2102.12694, arXiv.org.
    6. Harrison, J. Michael & Pliska, Stanley R., 1983. "A stochastic calculus model of continuous trading: Complete markets," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 313-316, August.
    7. Peng, Cheng & Li, Shuang & Zhao, Yanlong & Bao, Ying, 2021. "Sample average approximation of CVaR-based hedging problem with a deep-learning solution," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
    8. Alexandre Carbonneau & Frédéric Godin, 2021. "Equal risk pricing of derivatives with deep hedging," Quantitative Finance, Taylor & Francis Journals, vol. 21(4), pages 593-608, April.
    9. Ben Hambly & Renyuan Xu & Huining Yang, 2021. "Recent Advances in Reinforcement Learning in Finance," Papers 2112.04553, arXiv.org, revised Feb 2023.
    10. Igor Halperin, 2019. "The QLBS Q-Learner goes NuQLear: fitted Q iteration, inverse RL, and option portfolios," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1543-1553, September.
    11. Hirsa, Ali & Neftci, Salih N., 2013. "An Introduction to the Mathematics of Financial Derivatives," Elsevier Monographs, Elsevier, edition 3, number 9780123846822.
    12. Hull, John & White, Alan, 2017. "Optimal delta hedging for options," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 180-190.
    13. Ben Hambly & Renyuan Xu & Huining Yang, 2023. "Recent advances in reinforcement learning in finance," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 437-503, 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. 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.
    2. Ben Hambly & Renyuan Xu & Huining Yang, 2021. "Recent Advances in Reinforcement Learning in Finance," Papers 2112.04553, arXiv.org, revised Feb 2023.
    3. Wayne King Ming Chan, 2015. "RAROC-Based Contingent Claim Valuation," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2015, January-A.
    4. Wayne King Ming Chan, 2015. "RAROC-Based Contingent Claim Valuation," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 21, July-Dece.
    5. Ben Hambly & Renyuan Xu & Huining Yang, 2023. "Recent advances in reinforcement learning in finance," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 437-503, July.
    6. Reilly Pickard & Yuri Lawryshyn, 2023. "Deep Reinforcement Learning for Dynamic Stock Option Hedging: A Review," Mathematics, MDPI, vol. 11(24), pages 1-19, December.
    7. Timothy Johnson, 2015. "Reciprocity as a Foundation of Financial Economics," Journal of Business Ethics, Springer, vol. 131(1), pages 43-67, September.
    8. U. Cherubini & M. Esposito, 1995. "Options in and on interest rate futures contracts: results from martingale pricing theory," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(1), pages 1-16.
    9. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2016. "Must an optimal buy and hold strategy contain any derivative?," IC3JM - Estudios = Working Papers 23912, Instituto Mixto Carlos III - Juan March de Ciencias Sociales (IC3JM).
    10. N. Azevedo & D. Pinheiro & S. Z. Xanthopoulos & A. N. Yannacopoulos, 2018. "Who would invest only in the risk-free asset?," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-14, September.
    11. Jay Cao & Jacky Chen & Soroush Farghadani & John Hull & Zissis Poulos & Zeyu Wang & Jun Yuan, 2022. "Gamma and Vega Hedging Using Deep Distributional Reinforcement Learning," Papers 2205.05614, arXiv.org, revised Jan 2023.
    12. Jaime A. Londo~no, 2003. "State Tameness: A New Approach for Credit Constrains," Papers math/0305274, arXiv.org, revised Feb 2004.
    13. Balbás, Alejandro & Garrido, José & Okhrati, Ramin, 2016. "Good deal measurement in asset pricing: Actuarial and financial implications," IC3JM - Estudios = Working Papers 23546, Instituto Mixto Carlos III - Juan March de Ciencias Sociales (IC3JM).
    14. Hosam Ki & Byungwook Choi & Kook‐Hyun Chang & Miyoung Lee, 2005. "Option pricing under extended normal distribution," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(9), pages 845-871, September.
    15. 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.
    16. Tak Siu, 2006. "Option Pricing Under Autoregressive Random Variance Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 62-75.
    17. Wu, Bo & Li, Lingfei, 2024. "Reinforcement learning for continuous-time mean-variance portfolio selection in a regime-switching market," Journal of Economic Dynamics and Control, Elsevier, vol. 158(C).
    18. Elyès Jouini & Clotilde Napp, 2002. "Arbitrage Pricing And Equilibrium Pricing: Compatibility Conditions," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume III), chapter 6, pages 131-158, World Scientific Publishing Co. Pte. Ltd..
    19. Jos'e Manuel Corcuera, 2021. "The Golden Age of the Mathematical Finance," Papers 2102.06693, arXiv.org, revised Mar 2021.
    20. Carbonneau, Alexandre, 2021. "Deep hedging of long-term financial derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 327-340.

    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:eee:finlet:v:62:y:2024:i:pa:s1544612324001314. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/frl .

    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.