Financial Applications of Gaussian Processes and Bayesian Optimization

In the last five years, the financial industry has been impacted by the emergence of digitalization and machine learning. In this article, we explore two methods that have undergone rapid development in recent years: Gaussian processes and Bayesian optimization. Gaussian processes can be seen as a generalization of Gaussian random vectors and are associated with the development of kernel methods. Bayesian optimization is an approach for performing derivative-free global optimization in a small dimension, and uses Gaussian processes to locate the global maximum of a black-box function. The first part of the article reviews these two tools and shows how they are connected. In particular, we focus on the Gaussian process regression, which is the core of Bayesian machine learning, and the issue of hyperparameter selection. The second part is dedicated to two financial applications. We first consider the modeling of the term structure of interest rates. More precisely, we test the fitting method and compare the GP prediction and the random walk model. The second application is the construction of trend-following strategies, in particular the online estimation of trend and covariance windows.