  Options have provided a field of much study because of the complexity
involved in pricing them. The Black-Scholes equations were developed to price
options but they are only valid for European styled options. There is added
complexity when trying to price American styled options and this is why the use
of neural networks has been proposed. Neural Networks are able to predict
outcomes based on past data. The inputs to the networks here are stock
volatility, strike price and time to maturity with the output of the network
being the call option price. There are two techniques for Bayesian neural
networks used. One is Automatic Relevance Determination (for Gaussian
Approximation) and one is a Hybrid Monte Carlo method, both used with
Multi-Layer Perceptrons.
