Solving Black-Scholes equations with a neural network
Econophysics. Derivatives. European options. Neural networks.
The present work deals with a new methodology for pricing European options in the Brazilian market: the resolution of the Black-Scholes Equation through a Neural Network Multi Layer Perceptron. It is a supervised learning problem in which the response of the Neural Network is given by the resolution of the Differential Equation and the circumference conditions are the prices practiced in the Brazilian derivative market. It was verified that the Neural Network can learn from the data and presented better results than the analytical solution of Black-Scholes. The learning capacity of the Neural Network was also tested in comparison with ARIMA modeling and this was more accurate for short prediction horizons, but for larger horizons the neural network showed more satisfactory results.