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Option Pricing with Modular Neural Networks

Author

Listed:
  • Nikola Gradojevic

    (Faculty of Business Administration, Lakehead University)

  • Ramazan Gencay

    (Department of Economics, Simon Fraser University)

  • Dragan Kukolj

    (Faculty of Engineering, University of Novi Sad)

Abstract

This paper investigates a non-parametric modular neural network (MNN) model to price the S&P-500 European call options. The modules are based on time to maturity and moneyness of the options. The option price function of interest is homogenous of degree one with respect to the underlying index price and the strike price. When compared to an array of parametric and non-parametric models, the MNN method consistently exerts superior out-of-sample pricing performance. We conclude that modularity improves the generalization properties of standard feedforward neural network option pricing models (with and without the homogeneity hint).

Suggested Citation

  • Nikola Gradojevic & Ramazan Gencay & Dragan Kukolj, 2009. "Option Pricing with Modular Neural Networks," Working Paper series 32_09, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:32_09
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    Citations

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    Cited by:

    1. Gradojevic Nikola, 2016. "Multi-criteria classification for pricing European options," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(2), pages 123-139, April.
    2. Ke Nian & Thomas F. Coleman & Yuying Li, 2018. "Learning minimum variance discrete hedging directly from the market," Quantitative Finance, Taylor & Francis Journals, vol. 18(7), pages 1115-1128, July.
    3. Yang Qu & Ming-Xi Wang, 2019. "The option pricing model based on time values: an application of the universal approximation theory on unbounded domains," Papers 1910.01490, arXiv.org, revised Apr 2021.
    4. Yan Liu & Xiong Zhang, 2023. "Option Pricing Using LSTM: A Perspective of Realized Skewness," Mathematics, MDPI, vol. 11(2), pages 1-21, January.
    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. Yongxin Yang & Yu Zheng & Timothy M. Hospedales, 2016. "Gated Neural Networks for Option Pricing: Rationality by Design," Papers 1609.07472, arXiv.org, revised Mar 2020.
    7. Anindya Goswami & Nimit Rana, 2024. "A market resilient data-driven approach to option pricing," Papers 2409.08205, arXiv.org.
    8. Nikola Gradojevic, 2021. "Brexit and foreign exchange market expectations: Could it have been predicted?," Annals of Operations Research, Springer, vol. 297(1), pages 167-189, February.
    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. Johannes Ruf & Weiguan Wang, 2019. "Neural networks for option pricing and hedging: a literature review," Papers 1911.05620, arXiv.org, revised May 2020.
    11. Efe Arin & A. Murat Ozbayoglu, 2022. "Deep Learning Based Hybrid Computational Intelligence Models for Options Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 59(1), pages 39-58, January.
    12. Anindya Goswami & Sharan Rajani & Atharva Tanksale, 2020. "Data-Driven Option Pricing using Single and Multi-Asset Supervised Learning," Papers 2008.00462, arXiv.org, revised Dec 2020.
    13. Fei Chen & Charles Sutcliffe, 2012. "Pricing And Hedging Short Sterling Options Using Neural Networks," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 19(2), pages 128-149, April.
    14. Joseph L. Breeden & Eugenia Leonova, 2021. "Creating Unbiased Machine Learning Models by Design," JRFM, MDPI, vol. 14(11), pages 1-15, November.
    15. Ortíz Arango Francisco & Cabrera Llanos Agustín Ignacio & López Herrera Francisco, 2013. "Pronóstico de los índices accionarios DAX y S&P 500 con redes neuronales diferenciales," Contaduría y Administración, Accounting and Management, vol. 58(3), pages 203-225, julio-sep.
    16. Liu, Xiaoquan & Cao, Yi & Ma, Chenghu & Shen, Liya, 2019. "Wavelet-based option pricing: An empirical study," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1132-1142.
    17. Amine M. Aboussalah & Xuanze Li & Cheng Chi & Raj Patel, 2024. "The AI Black-Scholes: Finance-Informed Neural Network," Papers 2412.12213, arXiv.org.
    18. Hammad Siddiqi & Sajid Anwar, 2020. "The Pricing Kernel Puzzle: A Real Phenomenon or a Statistical Artifact?," International Review of Finance, International Review of Finance Ltd., vol. 20(2), pages 485-491, June.
    19. Dbouk, Wassim & Jamali, Ibrahim, 2018. "Predicting daily oil prices: Linear and non-linear models," Research in International Business and Finance, Elsevier, vol. 46(C), pages 149-165.
    20. Dragan Kukolj & Nikola Gradojevic & Camillo Lento, 2012. "Improving Non-Parametric Option Pricing during the Financial Crisis," Working Paper series 35_12, Rimini Centre for Economic Analysis.
    21. Lirong Gan & Wei-han Liu, 2024. "Option Pricing Based on the Residual Neural Network," Computational Economics, Springer;Society for Computational Economics, vol. 63(4), pages 1327-1347, April.
    22. Adamu Abubakar & Haruna Chiroma & Abdullah Khan & Mukhtar Fatihu Hamza & Ali Baba Dauda & Mahmood Nadeem & Shah Asadullah & Jaafar Zubairu Maitama & Tutut Herawan, 2016. "Utilizing Modular Neural Network for Prediction of Possible Emergencies Locations within Point of Interest of Hajj Pilgrimage," Modern Applied Science, Canadian Center of Science and Education, vol. 10(2), pages 1-34, February.
    23. Nikola Gradojevic & Dragan Kukolj & Ramazan Gencay, 2011. "Clustering and Classification in Option Pricing," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 3(2), pages 109-128, October.
    24. Muyang Ge & Shen Zhou & Shijun Luo & Boping Tian, 2021. "3D Tensor-based Deep Learning Models for Predicting Option Price," Papers 2106.02916, arXiv.org, revised Sep 2021.
    25. Gradojevic, Nikola & Kukolj, Dragan & Adcock, Robert & Djakovic, Vladimir, 2023. "Forecasting Bitcoin with technical analysis: A not-so-random forest?," International Journal of Forecasting, Elsevier, vol. 39(1), pages 1-17.

    More about this item

    Keywords

    Option Pricing; Modular Neural Networks; Non-parametric Methods;
    All these keywords.

    JEL classification:

    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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