Pricing European options using artificial neural networks

Abstract

The study’s focus is to examine the pricing of European options using artificial neural networks. It aims to use the predictive powers of artificial neural networks to forecast option prices for European puts and calls when presented with options data. For this investigation, two artificial neural networks the multi-layer perceptron neural network and the radial basis function neural network were employed. Since option price data are not readily available, the study uses Monte Carlo method to generate the data that is required for European put and call options training of the two artificial neural networks. These models are developed, tested and trained using simulated data and are then used to predict option prices. Training capability and comparisons are tested using several performance measures which include R2, MD, MAD, MSD and SMAPD. Numerical tests are used to estimate the generalisation capabilities of artificial neural networks. The findings from the neural network models numerical tests are compared with the analytical Black-Scholes model. Finally, what-if-analysis on the option prices as some of the option input parameters are varied is performed. The key outcomes of the study are that both the MLP and RBF neural network are very accurate at approximating the option prices. A closer look at the findings indicated that the MLP was a better fit to the data as compared to the RBF. This might be alluded to the use of ReLU activation function in the MLP which provided better learning for the MLP model as compared to the Gaussian radial basis function that was used for RBF. Numerical tests were carried out using the trained neural network models to predict the option prices and the findings were compared to the analytical Black-Scholes model. The findings reveal that the option prices obtained using the MLP are not considerably different from those of the Black-Scholes analytical model. However, the RBF model produced some option prices with considerably sizeable values different from the analytical values. Thus, the MLP was better at predicting option prices in comparison to the RBF. The study proposes a future related investigation into pricing European options using a different neural network structure and using a different analytical or numerical approach.