Gaussian Processes and Bayesian Optimization in Finance

Summary

The article introduces Gaussian processes (GPs) and Bayesian optimization, explaining how GP regression supports Bayesian machine learning and how its hyperparameters must be selected. Bayesian optimization uses a probabilistic model to search for an optimum in a black-box function without requiring derivatives, particularly when the number of parameters is small.

It describes two financial applications: fitting the term structure of interest rates, where GP predictions are compared with a random-walk model, and building trend-following strategies by estimating trend and covariance windows online. The stated comparisons show what the methods are evaluated against, but the excerpt gives no performance results, data details, or implementation choices. It therefore offers an overview of the tools and applications rather than enough evidence to judge predictive value, trading costs, or robustness.

Key ideas

• Gaussian processes extend Gaussian random vectors to functions and are used in kernel methods.
• Bayesian optimization uses a GP model to guide derivative-free searches for black-box optima.
• GP regression is central to the approach, and its hyperparameters require selection.
• The article applies GPs to interest-rate term structure fitting and compares predictions with a random walk.
• It also studies online selection of trend and covariance windows for trend-following strategies.

Tags

# Financial Applications of Gaussian Processes and Bayesian Optimization


# 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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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