Calibrating FBSDEs Driven Models in Finance via NNs

Luca Di Persio, Emanuele Lavagnoli and Marco Patacca
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Luca Di Persio: Department of Computer Science, University of Verona, via Ca’ Vignal 2, 37129 Verona, Italy
Emanuele Lavagnoli: Department of Computer Science, University of Verona, via Ca’ Vignal 2, 37129 Verona, Italy

Risks, 2022, vol. 10, issue 12, 1-19

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.

Keywords: Black–Scholes–Barenblatt; neural networks; stochastic volatility models (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2022
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