Forecasting portfolio-Value-at-Risk with mixed factorial hidden Markov models

This paper is concerned with the statistical modeling of the latent dependence and comovement structures of multivariate financial data using a new approach based on mixed factorial hidden Markov models, and their applications in Value-at-Risk (VaR) valuation. This approach combines hidden Markov Models (HMM) with mixed latent factor models. The HMM generates a piece-wise constant state evolution process and the observations are produced from the state vectors by a mixture of factor analyzers observation process. This new switching specification provides an alternative, compact, model to handle intra-frame correlation and unobserved heterogeneity in financial data. For maximum likelihood estimation we have proposed an iterative approach based on the Expectation-Maximisation (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 procedure, we found that this new specification exhibits a good fit to the data, improves the accuracy of VaR predictions and can avoid serious violations when a financial crisis occurs.