  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.
