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Pricing Options and Computing Implied Volatilities using Neural Networks

Author

Listed:
  • Shuaiqiang Liu

    (Delft Institute of Applied Mathematics (DIAM), Delft University of Technology, Building 28, Mourik Broekmanweg 6, 2628 XE Delft, The Netherlands)

  • Cornelis W. Oosterlee

    (Delft Institute of Applied Mathematics (DIAM), Delft University of Technology, Building 28, Mourik Broekmanweg 6, 2628 XE Delft, The Netherlands
    Centrum Wiskunde & Informatica, Science Park 123, 1098 XG Amsterdam, The Netherlands)

  • Sander M. Bohte

    (Centrum Wiskunde & Informatica, Science Park 123, 1098 XG Amsterdam, The Netherlands)

Abstract
This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent’s iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly.

Suggested Citation

  • Shuaiqiang Liu & Cornelis W. Oosterlee & Sander M. Bohte, 2019. "Pricing Options and Computing Implied Volatilities using Neural Networks," Risks, MDPI, vol. 7(1), pages 1-22, February.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:1:p:16-:d:204491
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    References listed on IDEAS

    as
    1. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    2. 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.
    3. Garcia, Rene & Gencay, Ramazan, 2000. "Pricing and hedging derivative securities with neural networks and a homogeneity hint," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 93-115.
    4. 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.
    5. Yao, Jingtao & Li, Yili & Tan, Chew Lim, 2000. "Option price forecasting using neural networks," Omega, Elsevier, vol. 28(4), pages 455-466, August.
    6. Fan, Jianqing & Mancini, Loriano, 2009. "Option Pricing With Model-Guided Nonparametric Methods," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1351-1372.
    7. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    machine learning; neural networks; computational finance; option pricing; implied volatility; GPU; Black-Scholes; Heston;
    All these keywords.

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics
    • M4 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting
    • K2 - Law and Economics - - Regulation and Business Law

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