In this article, we develop a new approach within the framework of asset pricing models that incorporates two key features of the latent volatility: co-movement among conditionally heteroscedastic financial returns and switching between different unobservable regimes. By combining latent factor models with hidden Markov chain models we derive a dynamical local model for segmentation and prediction of multivariate conditionally heteroscedastic financial time series. We concentrate more precisely on situations where the factor variances are modelled by univariate generalized quadratic autoregressive conditionally heteroscedastic processes. The expectation maximization algorithm that we have developed for the maximum likelihood estimation is based on a quasi-optimal switching Kalman filter approach combined with a generalized pseudo-Bayesian approximation, which yield inferences about the unobservable path of the common factors, their variances and the latent variable of the state process. Extensive Monte Carlo simulations and preliminary experiments obtained with daily foreign exchange rate returns of eight currencies show promising results.Traditionally, these issues were considered in a static framework, but recently, the emphasis has shifted towards inter-temporal asset pricing models in which agents decisions are based on the distribution of returns conditional on the available information, which is obviously changing. This is partly motivated by the fact that financial markets' volatility changes over time. However, it was not until Engle's [2] work on autoregressive conditional heteroscedasticity (ARCH) and Bollerslev's [3] generalized ARCH (GARCH) that researchers were able to take into account the time variation in the first and second moments of returns. Since then, several researchers have used Factor-ARCH models to provide a plausible and parsimonious parametrization of the time-varying variance-covariance structure of asset returns. For a review see Engle et al. [4], Engle and Ng [5], Diebold and Nerlove [6], Engle and Susmel [7], Demos and Sentana [8] and Lin [9].An assumption of these models is that the relationships between variables has not changed over time, but recent empirical works have shown that this assumption of structural stability is invalid for many financial and economic data sets [10]. In the financial econometric literature, models where structural change can be modelled endogenously have been proposed by Cai [11] and Hamilton and Susmel [12] for the Markov switching ARCH model, while So et al. [13] and Duker [14] have extended the Markov switching model to the stochastic volatility and GARCH frameworks, respectively. The model proposed by Hamilton and Susmel [12] allows the parameters of a univariate ARCH process to come from one of the several different regimes, with transitions between regimes governed by an unobserved Markov chain, in order to study the impact of large and small shocks on the volatility process of the US weekly stock returns. Alternatively, So et al. [13] have u...

Abstract. In this paper we develop a new approach within the framework of asset pricing models that incorporates two key features of the latent volatility: co-movement among conditionally heteroskedastic financial returns and switching between different unobservable regimes. By combining conditionally heteroskedastic factor models with hidden Markov chain models (HMM), we derive a dynamical local model for segmentation and prediction of multivariate conditionally heteroskedastic financial time series. The EM algorithm that we have developed for the maximum likelihood estimation, is based on a Viterbi approximation which yields inferences about the unobservable path of the common factors, their variances and the latent variable of the state process. Extensive Monte Carlo simulations and preliminary experiments obtained with a dataset on weekly average returns of closing spot prices for eight European currencies show promising results.

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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.