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An unsupervised deep learning approach in solving partial integro-differential equations

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  • Ali Hirsa
  • Weilong Fu

Abstract

We investigate solving partial integro-differential equations (PIDEs) using unsupervised deep learning in this paper. To price options, assuming underlying processes follow Levy processes, we require to solve PIDEs. In supervised deep learning, pre-calculated labels are used to train neural networks to fit the solution of the PIDE. In an unsupervised deep learning, neural networks are employed as the solution, and the derivatives and the integrals in the PIDE are calculated based on the neural network. By matching the PIDE and its boundary conditions, the neural network gives an accurate solution of the PIDE. Once trained, it would be fast for calculating options values as well as option Greeks.

Suggested Citation

  • Ali Hirsa & Weilong Fu, 2020. "An unsupervised deep learning approach in solving partial integro-differential equations," Papers 2006.15012, arXiv.org, revised Dec 2020.
    • Handle: RePEc:arx:papers:2006.15012
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    References listed on IDEAS

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    3. A Itkin, 2019. "Deep learning calibration of option pricing models: some pitfalls and solutions," Papers 1906.03507, arXiv.org.
    4. Weilong Fu & Ali Hirsa, 2019. "A fast method for pricing American options under the variance gamma model," Papers 1903.07519, arXiv.org.
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    6. 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.
    7. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    8. 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, arXiv.org.
    9. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
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    Cited by:

    1. Bastien Baldacci & Joffrey Derchu & Iuliia Manziuk, 2020. "An approximate solution for options market-making in high dimension," Papers 2009.00907, arXiv.org.

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