  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.
