Conformal prediction of option prices

Abstract

The uncertainty associated with option price predictions has largely been overlooked in the literature. This paper aims to fill this gap by quantifying such uncertainty using conformal prediction. Conformal prediction is a model-agnostic procedure that constructs prediction intervals, ensuring valid coverage in finite samples without relying on distributional assumptions. Through the simulation of synthetic option prices, we find that conformal prediction generates prediction intervals for gradient boosting machines with an empirical coverage close to the nominal level. Conversely, non-conformal prediction intervals exhibit empirical coverage levels that fall short of the nominal target. In other words, they fail to contain the actual option price more frequently than expected for a given coverage level. As anticipated, we also observe a decrease in the width of prediction intervals as the size of the training data increases. However, we uncover significant variations in the width of these intervals across different options. Specifically, out-of-the-money options and those with a short time-to-maturity exhibit relatively wider prediction intervals. Then, we perform an empirical study using American call and put options on individual stocks. We find that the empirical results replicate those obtained in the simulation experiment.