Neural Networks as Semiparametric Option Pricing Tool

We study the ability of artificial neural networks to price the European style call and put options on the S&P 500 index covering the daily data for the period from June 2004 to June 2007. The greatest advantage of option pricing with neural networks is that we do not need to make any assumptions about the volatility of the underlying asset. We divide the data set into several categories according to moneyness and time to maturity. Then, we price all options through the categories. The results show that neural networks outperform benchmark Black Scholes model with significantly lower pricing error across all categories for both call and put options. Moreover, the difference between Black Scholes and neural network errors significantly widens with deepness of moneyness or expiration. The deeper the option is in/out of the money and/or the longer the option has expiration, the greater is the difference between neural networks and Black Scholes errors. We show that neural networks can correct for the Black Scholes maturity and moneyness bias.