  One of the most discussed problems in the financial world is stock option
pricing. The Black-Scholes Equation is a Parabolic Partial Differential
Equation which provides an option pricing model. The present work proposes an
approach based on Neural Networks to solve the Black-Scholes Equations.
Real-world data from the stock options market were used as the initial boundary
to solve the Black-Scholes Equation. In particular, times series of call
options prices of Brazilian companies Petrobras and Vale were employed. The
results indicate that the network can learn to solve the Black-Sholes Equation
for a specific real-world stock options time series. The experimental results
showed that the Neural network option pricing based on the Black-Sholes
Equation solution can reach an option pricing forecasting more accurate than
the traditional Black-Sholes analytical solutions. The experimental results
making it possible to use this methodology to make short-term call option price
forecasts in options markets.
