Can neural networks learn the Black-Scholes model? A simplified approach

Abstract

Neural networks have been shown to learn complex relationships. It would be interesting to see if the networks can be trained to learn the nonlinear relationship underlying Black-Scholes type models. 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? Our results from a simplified neural networks approach are rather encouraging, but more for volatility outputs than for call prices.