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Option Pricing with Modular Neural Networks


  • 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)


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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    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. repec:eee:ejores:v:272:y:2019:i:3:p:1132-1142 is not listed on IDEAS
    3. Yongxin Yang & Yu Zheng & Timothy M. Hospedales, 2016. "Gated Neural Networks for Option Pricing: Rationality by Design," Papers 1609.07472,, revised Nov 2016.
    4. repec:eee:riibaf:v:46:y:2018:i:c:p:149-165 is not listed on IDEAS
    5. 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.
    6. Nikola Gradojevic & Dragan Kukolj & Ramazan Gencay, 2011. "Clustering and Classification in Option Pricing," Review of Economic Analysis, Rimini Centre for Economic Analysis, vol. 3(2), pages 109-128, October.
    7. 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.

    More about this item


    Option Pricing; Modular Neural Networks; Non-parametric Methods;

    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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