Machine Learning Applications to Valuation of Options on Non-liquid Markets

Recently, there has been a considerable interest in machine learning (ML) applications to valuation of options. The main motivation is the speed of calibration or, for example, calculation of the 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 parameters of an advanced stochastic model. In the second stage the calibrated volatility surface (or the model parameters) are used to value given exotic options, again using a trained NN (or another ML model). The NNs are typically trained "off-line" by sampling many model and market parameters´ combinations and calculating the options´ market values. In our research, we focus on the quite common situation of a non-liquid option market where we lack sufficiently many plain vanilla option quotations to calibrate the volatility surface, but we still need to value an exotic option or just a plain vanilla option subject to a more advanced stochastic model as it is typical on energy and carbon derivative markets. We show that it is possible to use selected moments of the underlying historical price return series complemented with a volatility risk premium estimate to value such options using the ML approach.