Applications of Gaussian Process Latent Variable Models in Finance

TL;DR

This paper introduces a novel Bayesian covariance estimator based on Gaussian Process Latent Variable Models, improving stability and interpretability in financial risk management when data is limited.

Contribution

It presents a non-linear extension of factor models using GP-LVMs with a Bayesian approach that reduces estimation errors in covariance matrices for finance.

Findings

Reduces covariance estimation errors in small sample scenarios

Provides interpretable parameters similar to market betas

Enhances risk management applications in finance

Abstract

Estimating covariances between financial assets plays an important role in risk management. In practice, when the sample size is small compared to the number of variables, the empirical estimate is known to be very unstable. Here, we propose a novel covariance estimator based on the Gaussian Process Latent Variable Model (GP-LVM). Our estimator can be considered as a non-linear extension of standard factor models with readily interpretable parameters reminiscent of market betas. Furthermore, our Bayesian treatment naturally shrinks the sample covariance matrix towards a more structured matrix given by the prior and thereby systematically reduces estimation errors. Finally, we discuss some financial applications of the GP-LVM.