IDEAS home Printed from https://ideas.repec.org/a/spr/orspec/v44y2022i3d10.1007_s00291-022-00672-1.html
   My bibliography  Save this article

Derivatives of feed-forward neural networks and their application in real-time market risk management

Author

Listed:
  • Antal Ratku

    (University of Freiburg
    Allianz Global Investors GmbH)

  • Dirk Neumann

    (Allianz Global Investors GmbH)

Abstract

Market risk management of financial derivatives requires the efficient calculation of their price sensitivities with respect to changes in market factors. This paper shows how a deep feed-forward neural network which has been trained for pricing derivative instruments can be efficiently used to calculate these sensitivities as well. The proposed method is a fast and easily implementable alternative approach to automatic differentiation, and it simultaneously calculates all the first- and second-order derivatives of a multilayer feed-forward neural network with respect to its input features. The paper quantifies the performance improvement of the proposed method over a recent, publicly available implementation of automatic differentiation for a wide range of network sizes. The number of input parameters in these networks corresponds to those of commonly used financial models with stochastic volatility. The numerical accuracy of the proposed sensitivity calculations is demonstrated with a case study, calculating price sensitivities of European options under stochastic volatility. While the paper focuses on financial applications, the results presented herein are applicable to all deep feed-forward neural networks with sufficiently smooth activation functions.

Suggested Citation

  • Antal Ratku & Dirk Neumann, 2022. "Derivatives of feed-forward neural networks and their application in real-time market risk management," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(3), pages 947-965, September.
    • Handle: RePEc:spr:orspec:v:44:y:2022:i:3:d:10.1007_s00291-022-00672-1
    DOI: 10.1007/s00291-022-00672-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00291-022-00672-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00291-022-00672-1?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. 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.
    2. Johannes Ruf & Weiguan Wang, 2019. "Neural networks for option pricing and hedging: a literature review," Papers 1911.05620, arXiv.org, revised May 2020.
    3. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    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. Raquel M. Gaspar & Sara D. Lopes & Bernardo Sequeira, 2020. "Neural Network Pricing of American Put Options," Risks, MDPI, vol. 8(3), pages 1-24, July.
    6. 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.
    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. Patrick Büchel & Michael Kratochwil & Maximilian Nagl & Daniel Rösch, 2022. "Deep calibration of financial models: turning theory into practice," Review of Derivatives Research, Springer, vol. 25(2), pages 109-136, July.
    2. Boris Ter-Avanesov & Homayoon Beigi, 2024. "MLP, XGBoost, KAN, TDNN, and LSTM-GRU Hybrid RNN with Attention for SPX and NDX European Call Option Pricing," Papers 2409.06724, arXiv.org, revised Oct 2024.
    3. A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2022. "Deep Stochastic Optimization in Finance," Papers 2205.04604, arXiv.org.
    4. 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.
    5. Ryno du Plooy & Pierre J. Venter, 2021. "A Comparison of Artificial Neural Networks and Bootstrap Aggregating Ensembles in a Modern Financial Derivative Pricing Framework," JRFM, MDPI, vol. 14(6), pages 1-18, June.
    6. Hui Chen & Antoine Didisheim & Simon Scheidegger, 2021. "Deep Structural Estimation: With an Application to Option Pricing," Papers 2102.09209, arXiv.org.
    7. Amine M. Aboussalah & Xuanze Li & Cheng Chi & Raj Patel, 2024. "The AI Black-Scholes: Finance-Informed Neural Network," Papers 2412.12213, arXiv.org.
    8. Kathrin Glau & Linus Wunderlich, 2020. "The Deep Parametric PDE Method: Application to Option Pricing," Papers 2012.06211, arXiv.org.
    9. Cao, Yi & Liu, Xiaoquan & Zhai, Jia, 2021. "Option valuation under no-arbitrage constraints with neural networks," European Journal of Operational Research, Elsevier, vol. 293(1), pages 361-374.
    10. Yanhui Shen, 2023. "American Option Pricing using Self-Attention GRU and Shapley Value Interpretation," Papers 2310.12500, arXiv.org.
    11. Jaegi Jeon & Kyunghyun Park & Jeonggyu Huh, 2021. "Extensive networks would eliminate the demand for pricing formulas," Papers 2101.09064, arXiv.org.
    12. Laurens Van Mieghem & Antonis Papapantoleon & Jonas Papazoglou-Hennig, 2023. "Machine learning for option pricing: an empirical investigation of network architectures," Papers 2307.07657, arXiv.org.
    13. Li, Gang & Zhang, Chu, 2013. "Diagnosing affine models of options pricing: Evidence from VIX," Journal of Financial Economics, Elsevier, vol. 107(1), pages 199-219.
    14. Masanori Hirano & Kentaro Imajo & Kentaro Minami & Takuya Shimada, 2023. "Efficient Learning of Nested Deep Hedging using Multiple Options," Papers 2305.12264, arXiv.org.
    15. Johannes Ruf & Weiguan Wang, 2020. "Hedging with Linear Regressions and Neural Networks," Papers 2004.08891, arXiv.org, revised Jun 2021.
    16. Maciej Wysocki & Robert Ślepaczuk, 2020. "Artificial Neural Networks Performance in WIG20 Index Options Pricing," Working Papers 2020-19, Faculty of Economic Sciences, University of Warsaw.
    17. Ballotta, Laura & Rayée, Grégory, 2022. "Smiles & smirks: Volatility and leverage by jumps," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1145-1161.
    18. Xia, Kun & Yang, Xuewei & Zhu, Peng, 2023. "Delta hedging and volatility-price elasticity: A two-step approach," Journal of Banking & Finance, Elsevier, vol. 153(C).
    19. Xianhua Peng & Xiang Zhou & Bo Xiao & Yi Wu, 2024. "A Risk Sensitive Contract-unified Reinforcement Learning Approach for Option Hedging," Papers 2411.09659, arXiv.org.
    20. S'andor Kuns'agi-M'at'e & G'abor F'ath & Istv'an Csabai & G'abor Moln'ar-S'aska, 2022. "Deep Weighted Monte Carlo: A hybrid option pricing framework using neural networks," Papers 2208.14038, arXiv.org, revised Dec 2022.

    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:spr:orspec:v:44:y:2022:i:3:d:10.1007_s00291-022-00672-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.