Bayesian Value-at-Risk with product partition models

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 for measuring and
controlling the market risk of an asset or portfolio, and 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 the
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.