Mixture models for VaR and stress testing

In this paper we deal with the use of multivariate normal mixture distributions to model asset returns, In particular, by modelling daily asset returns as a mixture of a low-volatility and a high-volatility distribution, we obtain three main results: (i) we can use posterior probabilities to identify hectic observations; (ii) we are able to compute a non-parametric fat-tails Value at Risk by sampling repeatedly from the mixture and computing the quantile of the empirical distribution; (iii) we can use the estimated parameters of the hectic distribution for stress testing purposes. We show how these three items can be addressed using either real data and simulation methods.