Mixture Of Probabilistic Factor Analyzers For Market Risk Measurement: Empirical Evidence From The Tunisian Foreign Exchange Market

Abstract

In this paper, we propose a new approach for Basel-Compliant Value-at-Risk (VaR) estimation in financial portfolio risk management, which combines Gaussian Mixture Models with probabilistic factor analysis models. This new mixed specification provides an alternative, compact, model to handle co-movements, heterogeneity and intra-frame correlations in financial data. This results in a model which concurrently performs clustering and dimensionality reduction, and can be considered as a reduced dimension mixture of probabilistic factor analyzers. For maximum likelihood estimation we have used an iterative approach based on the Alternating Expectation Conditional Maximization (AECM) algorithm. Using a set of historical data in a rolling time window, from the Tunisian foreign exchange market, the model structure as well as its parameters are determined and estimated. Then, the fitted model combined with a modified Monte-Carlo simulation algorithm was used to predict the VaR. Through a Backtesting analysis, we found that this new specification exhibits a good fit to the data compared to other competing approaches, improves the accuracy of VaR prediction, possesses more flexibility, and can avoid serious violations when a financial crisis occurs.