Artificial neural networks applied to option pricing

Abstract

Artificial Neural Networks has seen tremendous growth in recent years. It has been applied to various sciences, including applied mathematics, chemistry, physics, and engineering and has also been implemented in various areas of finance. Many researchers have applied them to forecasting of stock prices and other fields of finance. In this study we focus on option pricing. An option is a contract giving the buyer of the contract the right but not the obligation to purchase stock on or before a certain expiration date. Options have become a multi-billion dollar industry in modern times, and there has been a lot of focus on pricing these option contracts. Option pricing data is highly non-linear and its pricing has its basis in stochastic calculus. Since neural networks have excellent non-linear modeling capabilities, it seems obvious to apply neural networks to option pricing. In this thesis, many different methodologies are developed to model the data. The multilayer perceptron and radial basis functions are used in the stand-alone neural networks. Then, the architectures of the stand-alone networks are optimized using particle swarm optimization, which leads to excellent results. Thereafter, a committee of neural networks is investigated.

A committee network is an average of a combination of stand-alone neural networks. In contrast to stand-alone networks, a committee network has great generalization capabilities.

Many different methods are developed for attaining optimal results from these committee networks. The methods included different forms of weighting the stand-alone networks, a non-linear combination of the committee members using another stand-alone neural network, a two layer committee network where the second layer was used for smoothing the output and a circular committee network. Lastly, genetic algorithm, with the Metropolis-Hastings algorithm, was used to optimize the committee of neural networks. Finally all these methods were analyzed.