Solving Black-Scholes equations with a neural network
Option Pricing, Black-Scholes Model, Neural Networks.
The Black-Scholes option pricing model is based on a Parabolic Partial Differential Equation which only provides analytical solution for the case of European options. The present work transforms the Black-Scholes equation into the heat equation and solves it using an MLP neural network. For the training of the network, a series of call option prices of Brazilian companies were used, Petrobras and Vale. The mathematical operations carried out in the Black-Scholes equation were applied to the option prices, in order to carry out comparisons between the real prices and the prices estimated by the neural network. The results indicate that the network can learn with the help of real data to solve the Black-Scholes equation, making it possible to use this methodology to make shortterm call option price forecasts in options markets.