Machine Learning Applications for the Valuation of Options on Non-Liquid Option Markets

Recently, there has been considerable interest in machine learning (ML) applications for the valuation of options. The main motivation is the speed of calibration or, for example, the calculation of credit valuation adjustments (CVA). It is usually assumed that there is a relatively liquid market with plain vanilla option quotations that can be used to calibrate (using an ML model) the volatility surface or to estimate the parameters of an advanced stochastic model. In the second stage, the calibrated volatility surface (or the model parameters) is used to value given exotic options, again using a trained neural network (NN) or another ML model. The NNs are typically trained offline by sampling many model and market parameter combinations and calculating the options' market values. In this research, the authors focus on the quite common situation of a nonliquid option market in which one lacks a sufficient number of plain vanilla option quotations to calibrate the volatility surface, but one still needs to value an exotic option, or just a plain vanilla option, subject to a more advanced stochastic model, as is typical for energy and carbon derivatives markets. Their study shows that the historical return moment-based pricing and calibration NNs can be applicable in practice with a performance lower than but still comparable to the option-based calibration. The authors also demonstrate that the performance can be substantially improved when high-frequency historical data, allowing them to apply the concept of realized volatility, are available.