Bayesian Analysis of Value-at-Risk with Product Partition Models

TL;DR

This paper introduces a Bayesian approach using Product Partition Models for calculating Value-at-Risk, effectively handling outliers and providing detailed data clustering insights, demonstrated on Italian stock market data.

Contribution

It presents a novel Bayesian methodology for VaR computation using Product Partition Models, offering closed-form solutions and enhanced data clustering analysis.

Findings

Effective handling of outliers in VaR estimation.

Closed-form expression for VaR using Product Partition Models.

Rich information on data clustering and outliers obtained.

Abstract

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.