# Machine Learning for Pricing American Options in High-Dimensional Markovian and non-Markovian models

## TL;DR

This paper introduces two machine learning-based methods, GPR Tree and GPR Exact Integration, for efficiently pricing high-dimensional American basket options, including in non-Markovian models like rough Bergomi, demonstrating high accuracy and reliability.

## Contribution

The paper presents novel GPR Tree and GPR Exact Integration techniques that effectively handle high-dimensional and non-Markovian American option pricing problems.

## Key findings

- Methods are accurate for large baskets of assets.
- Techniques work well with non-Markovian models like rough Bergomi.
- Approaches outperform traditional methods in computational efficiency.

## Abstract

In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black-Scholes dynamics. The proposed techniques, called GPR Tree (GRP-Tree) and GPR Exact Integration (GPR-EI), are both based on Machine Learning, exploited together with binomial trees or with a closed formula for integration. Moreover, these two methods solve the backward dynamic programming problem considering a Bermudan approximation of the American option. On the exercise dates, the value of the option is first computed as the maximum between the exercise value and the continuation value and then approximated by means of Gaussian Process Regression. The two methods mainly differ in the approach used to compute the continuation value: a single step of binomial tree or integration according to the probability density of the process. Numerical results show that these two methods are accurate and reliable in handling American options on very large baskets of assets. Moreover we also consider the rough Bergomi model, which provides stochastic volatility with memory. Despite this model is only bidimensional, the whole history of the process impacts on the price, and handling all this information is not obvious at all. To this aim, we present how to adapt the GPR-Tree and GPR-EI methods and we focus on pricing American options in this non-Markovian framework.