Improving the Interpretability of Artificial Neural Networks Using the Example of the Pricing Options Problems

In this paper, we demonstrate how to improve the interpretability of neural networks using standard problems of computational finance as an example. In our first approach, we justify that a feedforward neural network with one hidden layer and positive weights is a natural approximator for general cumulative distribution functions of continuous random variables. Using this kind of interpretation, we design a neural network architecture that, as a result of training, leads to a neural network analogue of the classical Black–Scholes formula. The main advantage of our second approach for the numerical solution of the Black–Scholes equation is that, based on theoretically justified formulas for the approximating neural network, we can analytically calculate the loss function at each training iteration.