MIXTURE OF PROBABILISTIC FACTOR ANALYZERS FOR MARKET RISK MEASUREMENT: EMPIRICAL EVIDENCE FROM THE TUNISIAN FOREIGN EXCHANGE MARKET

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Mohamed Nidhal Mosbahi, Mohamed Saidane, Sarra Messabeb

https://doi.org/10.22495/rgcv7i2c1p4

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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.

Keywords: Value-at-Risk, Gaussian Mixture Model, Latent Factor Model, Mixture of Factor Analyzers, AECM Algorithm, Monte Carlo simulation, FX Market

Received: 05.02.2016
Accepted: 23.03.2017

How to cite this paper: Mosbahi, M. N., Saidane, M., Messabeb, S. (2017). Mixture Of Probabilistic Factor Analyzers For Market Risk Measurement: Empirical Evidence From The Tunisian Foreign Exchange Market. Risk governance & control: financial markets & institutions, 7(2-1), 158-169. https://doi.org/10.22495/rgcv7i2c1p4