On the Solution of the Black–Scholes Equation Using Feed-Forward Neural Networks

Saadet Eskiizmirliler (), Korhan Günel () and Refet Polat ()
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Saadet Eskiizmirliler: Yasar University
Korhan Günel: Aydın Adnan Menderes University
Refet Polat: Yasar University

Computational Economics, 2021, vol. 58, issue 3, No 15, 915-941

Abstract: Abstract This paper deals with a comparative numerical analysis of the Black–Scholes equation for the value of a European call option. Artificial neural networks are used for the numerical solution to this problem. According to this method, we approximate the unknown function of the option value using a trial function, which depends on a neural network solution and satisfies the given boundary conditions of the Black–Scholes equation. We consider some optimization methods, not examined in the standard literature, such as particle swarm optimization and the gradient-type monotone iteration process, to obtain the unknown parameters of the neural network. Numerical results show that this proposed version of neural network method obtains all data from the terminal value and boundary conditions with sufficient accuracy.

Keywords: Black–Scholes equation; Option pricing; Neural networks; Particle swarm optimization; Gradient descent; MSC 91G80; MSC 35Q91 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10614-020-10070-w

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