Financial Applications of Gaussian Processes and Bayesian Optimization

Abstract

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.

Bayesian Optimization for Parameter of Discrete Weibull Regression

“…Another acquisition functions was discussed by [2]; they are entropy-based acquisition functions in the study by [22], the earlier works of [9] has proven to have taken care of the challenges identified in the works of [22]. In achieve that, [9] proposed technique called predictive entropy search (PES).…”

“…BO can be used in a case where the objective function is vague. [1,2] pointed out that for black box optimization to take place all dimensions should have bounds on the search space. Bayesian optimization broadly looks into right combinations of hyperparamters that will yield maximum accuracy [3,4] or minimize loss such as computational cost.…”

“…The works of [5] showed the case of minimizing uncertainty using BO technique. Also, [6,7,2] demonstrated the usefulness of machine learning and Bayesian Optimization in finance and portfolio management respectively.…”

Machine Learning Optimization Algorithms & Portfolio Allocation

“…x i ln x i ≥ SE − 35 An example is the 5/10/40 UCITS rule: A UCITS fund may invest no more than 10% of its net assets in transferable securities or money market instruments issued by the same body, with a further aggregate limitation of 40% of net assets on exposures of greater than 5% to single issuers. 36 In this case, it is equivalent to maximize Shannon's entropy becausex = 1n.…”

Gaussian Process Imputation of Multiple Financial Series

“…Financial applications of artificial intelligence research has become an area of rapid development that strives to forecast financial indicators and performance metrics using machine learning (ML) with promising results [1, 2, 3,4]. Traditionally, financial indicators have been modelled using ARCH or GARCH models [5,6,7].…”