Financial Applications of Gaussian Processes and Bayesian Optimization

42 Pages Posted: 3 Apr 2019

See all articles by Joan Gonzalvez

Joan Gonzalvez

Ecole Normale Supérieure (ENS) de Lyon; Amundi Asset Management

Edmond Lezmi

Amundi Asset Management

Thierry Roncalli

Amundi Asset Management; University of Evry

Jiali Xu

Societe Generale

Date Written: February 28, 2019

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.

Keywords: Gaussian process, Bayesian optimization, machine learning, kernel function, hyperparameter selection, regularization, time-series prediction, asset allocation, portfolio optimization, trend-following strategy, moving-average estimator, ADMM, Cholesky trick

JEL Classification: C61, C63, G11

Suggested Citation

Gonzalvez, Joan and Lezmi, Edmond and Roncalli, Thierry and Xu, Jiali, Financial Applications of Gaussian Processes and Bayesian Optimization (February 28, 2019). Available at SSRN: https://ssrn.com/abstract=3344332 or http://dx.doi.org/10.2139/ssrn.3344332

Joan Gonzalvez

Ecole Normale Supérieure (ENS) de Lyon ( email )

15, parvis Rene Descartes BP 7000
Lyon Cedex 07, 69342
France

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

Edmond Lezmi

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

Thierry Roncalli (Contact Author)

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

University of Evry ( email )

Boulevard Francois Mitterrand
F-91025 Evry Cedex
France

Jiali Xu

Societe Generale ( email )

52 Place de l'Ellipse
La Défense, 92000
France

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