Relevance and Sensitivity Analysis of the inputs of a Multilayer Perceptron with application to option pricing

Abstract

Neural networks keep exhibiting superior predictive performance compared to other machine learning methods in the field of finance. They do not require construction of the complex models and fulfilment of strict economic assumptions, however, their application is often limited due to the lack of interpretability. A lot of studies were performed on addressing this problem, since an understanding of the network’s decision-making process would enable a more refine control over it and introduction of improvements, making achievement of desirable results easier. The “black box” problem can be illuminated by providing an explanatory insight into the relative influence of input variables. In classical feedforward neural networks, such as Multilayer Perceptron, neurons of the input correspond to features of the training patterns, number of which may be large, besides, not all of them may contain meaningful information. Thus, the contribution of the input variables to the output needs to be examined, after which the selection of inputs could be performed. After the detailed review of the literature, several methods to perform this procedure were described, compared, and criticized. The experiment performed included the application of some of these methods in the task of applying the Multilayer Perceptron to option pricing. Classical Black-Sholes model was compared to the performance of the single hidden layer neural network both on simulated and real market data in Python. Subsequently, significance testing of the option Greeks was done to prove meaningfulness of the results. Received outcomes point out interesting properties of the proposed approach of the input variables assessment and give valuable findings for the future research.