  In this paper we propose a novel Bayesian methodology for Value-at-Risk
computation based on parametric Product Partition Models. Value-at-Risk is a
standard tool to measure and control the market risk of an asset or a
portfolio, and it is also required for regulatory purposes. Its popularity is
partly due to the fact that it is an easily understood measure of risk. The use
of Product Partition Models allows us to remain in a Normal setting even in
presence of outlying points, and to obtain a closed-form expression for
Value-at-Risk computation. We present and compare two different scenarios: a
product partition structure on the vector of means and a product partition
structure on the vector of variances. We apply our methodology to an Italian
stock market data set from Mib30. The numerical results clearly show that
Product Partition Models can be successfully exploited in order to quantify
market risk exposure. The obtained Value-at-Risk estimates are in full
agreement with Maximum Likelihood approaches, but our methodology provides
richer information about the clustering structure of the data and the presence
of outlying points.
