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 model.
Covariance matrix estimation of financial assets with Gaussian Process Latent Variable Models Illustrates how the Gaussian Process Latent Variable Model (GP-LVM) can replace classical linear factor models for the estimation of covariance matrices in portfolio optimization problems. This paper uses standard GPLVMs to model the covariance structure and a latent space representation of S&P500 financial time series, to optimize portfolios and predict missing values. This paper proposes to use a GPLVM to model financial returns