Leveraging Machine Learning for High-Dimensional Option Pricing within the Uncertain Volatility Model

This paper explores the application of Machine Learning techniques for pricing high-dimensional options within the framework of the Uncertain Volatility Model (UVM). The UVM is a robust framework that accounts for the inherent unpredictability of market volatility by setting upper and lower bounds on volatility and the correlation among underlying assets. By leveraging historical data and extreme values of estimated volatilities and correlations, the model establishes a confidence interval for future volatility and correlations, thus providing a more realistic approach to option pricing. By integrating advanced Machine Learning algorithms, we aim to enhance the accuracy and efficiency of option pricing under the UVM, especially when the option price depends on a large number of variables, such as in basket or path-dependent options. Our approach evolves backward in time, dynamically selecting at each time step the most expensive volatility and correlation for each market state. Specifically, it identifies the particular values of volatility and correlation that maximize the expected option value at the next time step. This is achieved through the use of Gaussian Process regression, the computation of expectations via a single step of a multidimensional tree and the Sequential Quadratic Programming optimization algorithm. The numerical results demonstrate that the proposed approach can significantly improve the precision of option pricing and risk management strategies compared with methods already in the literature, particularly in high-dimensional contexts.