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Calibrating FBSDEs Driven Models in Finance via NNs

Author

Listed:
  • Luca Di Persio

    (Department of Computer Science, University of Verona, via Ca’ Vignal 2, 37129 Verona, Italy
    These authors contributed equally to this work.)

  • Emanuele Lavagnoli

    (Department of Computer Science, University of Verona, via Ca’ Vignal 2, 37129 Verona, Italy
    These authors contributed equally to this work.)

  • Marco Patacca

    (Department of Economics and Finance, University of Rome Tor Vergata, via Columbia 2, 00133 Rome, Italy
    These authors contributed equally to this work.)

Abstract

The curse of dimensionality problem refers to a set of troubles arising when dealing with huge amount of data as happens, e.g., applying standard numerical methods to solve partial differential equations related to financial modeling. To overcome the latter issue, we propose a Deep Learning approach to efficiently approximate nonlinear functions characterizing financial models in a high dimension. In particular, we consider solving the Black–Scholes–Barenblatt non-linear stochastic differential equation via a forward-backward neural network, also calibrating the related stochastic volatility model when dealing with European options. The obtained results exhibit accurate approximations of the implied volatility surface. Specifically, our method seems to significantly reduce the neural network’s training time and the approximation error on the test set.

Suggested Citation

  • Luca Di Persio & Emanuele Lavagnoli & Marco Patacca, 2022. "Calibrating FBSDEs Driven Models in Finance via NNs," Risks, MDPI, vol. 10(12), pages 1-19, November.
    • Handle: RePEc:gam:jrisks:v:10:y:2022:i:12:p:227-:d:989166
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    References listed on IDEAS

    as
    1. Maximilien Germain & Huyên Pham & Xavier Warin, 2021. "Neural networks-based algorithms for stochastic control and PDEs in finance ," Working Papers hal-03115503, HAL.
    2. Maximilien Germain & Huyên Pham & Xavier Warin, 2021. "Neural networks-based algorithms for stochastic control and PDEs in finance ," Post-Print hal-03115503, HAL.
    3. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    4. Christian Bayer & Benjamin Stemper, 2018. "Deep calibration of rough stochastic volatility models," Papers 1810.03399, arXiv.org.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Maximilien Germain & Huy^en Pham & Xavier Warin, 2021. "Neural networks-based algorithms for stochastic control and PDEs in finance," Papers 2101.08068, arXiv.org, revised Apr 2021.
    7. Jiequn Han & Ruimeng Hu, 2021. "Recurrent Neural Networks for Stochastic Control Problems with Delay," Papers 2101.01385, arXiv.org, revised Jun 2021.
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