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Supervised Deep Neural Networks (DNNs) for Pricing/Calibration of Vanilla/Exotic Options Under Various Different Processes


  • Ali Hirsa
  • Tugce Karatas
  • Amir Oskoui


We apply supervised deep neural networks (DNNs) for pricing and calibration of both vanilla and exotic options under both diffusion and pure jump processes with and without stochastic volatility. We train our neural network models under different number of layers, neurons per layer, and various different activation functions in order to find which combinations work better empirically. For training, we consider various different loss functions and optimization routines. We demonstrate that deep neural networks exponentially expedite option pricing compared to commonly used option pricing methods which consequently make calibration and parameter estimation super fast.

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  • Ali Hirsa & Tugce Karatas & Amir Oskoui, 2019. "Supervised Deep Neural Networks (DNNs) for Pricing/Calibration of Vanilla/Exotic Options Under Various Different Processes," Papers 1902.05810,
  • Handle: RePEc:arx:papers:1902.05810

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    References listed on IDEAS

    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
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    6. Jan Vecer & Mingxin Xu, 2004. "Pricing Asian options in a semimartingale model," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 170-175.
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    8. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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    Cited by:

    1. Jaegi Jeon & Kyunghyun Park & Jeonggyu Huh, 2021. "Extensive networks would eliminate the demand for pricing formulas," Papers 2101.09064,
    2. Johannes Ruf & Weiguan Wang, 2019. "Neural networks for option pricing and hedging: a literature review," Papers 1911.05620,, revised May 2020.
    3. Shuaiqiang Liu & Anastasia Borovykh & Lech A. Grzelak & Cornelis W. Oosterlee, 2019. "A neural network-based framework for financial model calibration," Papers 1904.10523,
    4. Longbing Cao, 2021. "AI in Finance: Challenges, Techniques and Opportunities," Papers 2107.09051,
    5. Ali Hirsa & Weilong Fu, 2020. "An unsupervised deep learning approach in solving partial integro-differential equations," Papers 2006.15012,, revised Dec 2020.
    6. Weilong Fu & Ali Hirsa, 2019. "A fast method for pricing American options under the variance gamma model," Papers 1903.07519,

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