Compare of linear and neural networks models for estimating and forecasting Black-Scholes option pricing model

Abstract

The Black-Scholes formula is a well-known model for pricing and hedging derivative securities. Interesting hypothetical questions that can be raised are: If option pricing model had not been developed, could a technique like neural networks have learnt the nonlinear form of the Black-Scholes type model to yield the fair value of an option? Could the networks have learnt to produce efficient implied volatility estimates? The results in this article from a simplified neural networks approach are rather encouraging, but more for volatility outputs than for call prices. This article will evaluate the performance of alternative neural network models relative to the standard linear model for forecasting relatively complex artificially generated time series. The article shows that relatively simple feedforward neural nets outperform the linear models in some cases, or do not do worse than the linear models.