Considering Appropriate Input Features of Neural Network to Calibrate Option Pricing Models

Abstract

Parameter estimation is crucial in using option pricing models, but it is often an ill-conditioned problem. While it has been demonstrated that neural networks can enhance the efficiency of multiple tasks, when performing parameter estimation using option prices data, the neural network approaches are fundamentally vulnerable because the task is one of the ill-conditioned problems. To address the issue, we propose a bijective transformation of the input features of a neural network to transform the ill-conditioned problem into an equivalent well-conditioned problem. This transformation can be simply summarized as using the corresponding implied volatilities as input features instead of option prices. Experiments have shown that the estimation network that use the transformed values as network inputs have significantly improved efficiency compared to the network that use the original values.