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Deep Local Volatility

Author

Listed:
  • Marc Chataigner
  • Stéphane Crépey

    (UFR Mathématiques UPCité - UFR Mathématiques [Sciences] - Université Paris Cité - UPCité - Université Paris Cité, LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité)

  • Matthew Dixon

Abstract

Deep learning for option pricing has emerged as a novel methodology for fast computations with applications in calibration and computation of Greeks. However, many of these approaches do not enforce any no-arbitrage conditions, and the subsequent local volatility surface is never considered. In this article, we develop a deep learning approach for interpolation of European vanilla option prices which jointly yields the full surface of local volatilities. We demonstrate the modification of the loss function or the feed forward network architecture to enforce (hard constraints approach) or favor (soft constraints approach) the no-arbitrage conditions and we specify the experimental design parameters that are needed for adequate performance. A novel component is the use of the Dupire formula to enforce bounds on the local volatility associated with option prices, during the network fitting. Our methodology is benchmarked numerically on real datasets of DAX vanilla options.

Suggested Citation

  • Marc Chataigner & Stéphane Crépey & Matthew Dixon, 2020. "Deep Local Volatility," Post-Print hal-03910122, HAL.
    • Handle: RePEc:hal:journl:hal-03910122
    DOI: 10.3390/risks8030082
    Note: View the original document on HAL open archive server: https://hal.science/hal-03910122
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    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. Garcia, Rene & Gencay, Ramazan, 2000. "Pricing and hedging derivative securities with neural networks and a homogeneity hint," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 93-115.
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    Cited by:

    1. Marc Chataigner & Areski Cousin & St'ephane Cr'epey & Matthew Dixon & Djibril Gueye, 2022. "Beyond Surrogate Modeling: Learning the Local Volatility Via Shape Constraints," Papers 2212.09957, arXiv.org.

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