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Hedging with Linear Regressions and Neural Networks

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  • Johannes Ruf
  • Weiguan Wang

Abstract

We study neural networks as nonparametric estimation tools for the hedging of options. To this end, we design a network, named HedgeNet, that directly outputs a hedging strategy. This network is trained to minimise the hedging error instead of the pricing error. Applied to end-of-day and tick prices of S&P 500 and Euro Stoxx 50 options, the network is able to reduce the mean squared hedging error of the Black-Scholes benchmark significantly. However, a similar benefit arises by simple linear regressions that incorporate the leverage effect.

Suggested Citation

  • Johannes Ruf & Weiguan Wang, 2020. "Hedging with Linear Regressions and Neural Networks," Papers 2004.08891, arXiv.org, revised Jun 2021.
    • Handle: RePEc:arx:papers:2004.08891
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    References listed on IDEAS

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    1. Carol Alexander & Alexander Rubinov & Markus Kalepky & Stamatis Leontsinis, 2012. "Regime‐dependent smile‐adjusted delta hedging," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(3), pages 203-229, March.
    2. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    3. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Do Call Prices and the Underlying Stock Always Move in the Same Direction?," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 549-584.
    4. Hutchinson, James M & Lo, Andrew W & Poggio, Tomaso, 1994. "A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks," Journal of Finance, American Finance Association, vol. 49(3), pages 851-889, July.
    5. Rama Cont & Yu Hang Kan, 2011. "Dynamic hedging of portfolio credit derivatives," Post-Print hal-00578008, HAL.
    6. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    7. Tankov, Peter & Voltchkova, Ekaterina, 2009. "Asymptotic analysis of hedging errors in models with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2004-2027, June.
    8. Johannes Ruf & Weiguan Wang, 2019. "Neural networks for option pricing and hedging: a literature review," Papers 1911.05620, arXiv.org, revised May 2020.
    9. Boyle, Phelim P. & Emanuel, David, 1980. "Discretely adjusted option hedges," Journal of Financial Economics, Elsevier, vol. 8(3), pages 259-282, September.
    10. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    11. Stephan Denkl & Martina Goy & Jan Kallsen & Johannes Muhle-Karbe & Arnd Pauwels, 2013. "On the performance of delta hedging strategies in exponential L�vy models," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1173-1184, July.
    12. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "When Is Time Continuous?," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 3, pages 71-102, World Scientific Publishing Co. Pte. Ltd..
    13. Claeskens G. & Hjort N.L., 2003. "The Focused Information Criterion," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 900-916, January.
    14. Hull, John & White, Alan, 2017. "Optimal delta hedging for options," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 180-190.
    15. 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.
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    Cited by:

    1. Samuel N. Cohen & Derek Snow & Lukasz Szpruch, 2021. "Black-box model risk in finance," Papers 2102.04757, arXiv.org.
    2. Xiaofei Shi & Daran Xu & Zhanhao Zhang, 2021. "Deep Learning Algorithms for Hedging with Frictions," Papers 2111.01931, arXiv.org, revised Dec 2022.
    3. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2022. "Hedging option books using neural-SDE market models," Papers 2205.15991, arXiv.org.
    4. Takayuki Sakuma, 2020. "Application of deep quantum neural networks to finance," Papers 2011.07319, arXiv.org, revised May 2022.
    5. A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2023. "Deep stochastic optimization in finance," Digital Finance, Springer, vol. 5(1), pages 91-111, March.
    6. Xiaofei Shi & Daran Xu & Zhanhao Zhang, 2023. "Deep learning algorithms for hedging with frictions," Digital Finance, Springer, vol. 5(1), pages 113-147, March.

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