Pricing Options in the Heston Model Using Artificial Neural Networks

The article considers numerical methods for pricing options in the Heston model. The main attention is paid to solving the Cauchy problem for the partial differential equation for option prices using artificial neural networks. The possibility of approximating the solution using feedforward neural networks with one hidden layer and sigmoid activation function is substantiated. The advantage of the proposed method is the ability to explicitly calculate loss functions when choosing the logistic regression as an activation function. The loss function of neural networks tracks errors in the execution of equations for option prices and approximation of initial conditions. For comparison method of solving the boundary value problem, Monte-Carlo method and method based on recurrent formulas on a binary tree are used. Computational experiments show that even with a moderate number of neurons in the hidden mode, the neural network approximates the prices of European in-the-money options quite well.