This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent’s iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly.

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Keywords Black-Scholes, Computational finance, GPU, Heston, Implied volatility, Machine learning, Neural networks, Option pricing
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Journal Risks
Liu, S, Oosterlee, C.W, & Bohte, S.M. (2019). Pricing options and computing implied volatilities using neural networks. Risks, 7(1). doi:10.3390/risks7010016