Abstract
The normal probability distribution assumption, to model price changes in Finance, belongs to the largest imperfections in the Value-at-Risk (VaR) estimation. In fact, the financial returns are rather distributed leptokurtic than normally and the empirical distributions are often skewed. In these cases, the normal distribution assumption results in over or underestimation of VaR especially when the quantiles are very high/low. Therefore, it is necessary to put emphasis on respecting the leptokurtic and skewed return distribution. In this paper, we propose a new approach for portfolio VaR estimation, which combines the standard latent factor model with the generalized quadratic autoregressive conditionally heteroskedastic model (GQARCH). This new "hybrid" specification provides an alternative, compact, model to handle co-movements, heteroskedasticity and intra-frame correlations in financial data. For maximum likelihood estimation we have used an iterative approach based on an extended version of the Kalman filter algorithm combined with the Expectation Maximization (EM) algorithm. Using a set of historical data, from the Tunisian foreign exchange market, the model parameters are estimated. Then, the fitted model combined with a modified Monte-Carlo simulation algorithm was used to predict the VaR of the Tunisian public debt portfolio. Through a Backtesting analysis, we found that this new specification produces far more accurate forecasts for the VaR compared to the mixture of factor analyzers and other competing approaches.