Abstract

During the recent credit crunch and the aftermath of the financial crisis it has become even more evident than before, that there is a need for accurate estimation of financial uncertainty. This is usually translated into estimating the volatility or variance of associated financial instruments, such as asset returns. In particular, there is increasing interest in large data sets with the objective of identifying similarities between asset returns, pinpointing highly volatile assets and thus identifying and measuring financial risk.

In this talk, I will define a suitable stochastic volatility model based on Wishart autoregressive processes. Such processes are natural models for estimating covariance matrices and their theoretical background has only been recently developed. We propose a sequential Monte Carlo algorithm, based on an auxiliary particle filter. We discuss the problem of unknown parameter estimation in the particle filter, and we provide modifications to existing procedures to deal with the large number of such parameters. We address the problem of model comparison in this particular application by considering several alternative models. Our findings suggest that particle filters are very useful in this context, overcoming most of the shortcomings of alternative models.