Machine learning over the free-parameters of the Black-Scholes equation: Stock market and Option market

The Black-Scholes equation is famous for predicting values for the prices of Options inside the stock market scenario. However, it has the limitation of depending on the estimated value for the volatility. On the other hand, several Machine learning techniques have been employed for predicting the values of the same quantity. In this paper we analyze some fundamental properties of the Black-Scholes equation and we then propose a way to train its free-parameters, the volatility in particular. This with the purpose of using this parameter as the fundamental one to be learned by a Machine Learning system and then improve the predictions in the stock market.