Search results

The BEKK GARCH class of models presents a popular set of tools for applied analysis of dynamic conditional covariances. Within this class the analyst faces a range of model choices that trade off flexibility with parameter parsimony. In the most flexible unrestricted BEKK the parameter dimensionality increases quickly with the number of variables. Covariance targeting decreases model dimensionality but induces a set of nonlinear constraints on the underlying parameter space that are difficult to implement. Recently, the rotated BEKK (RBEKK) has been proposed whereby a targeted BEKK model is applied after the spectral decomposition of the conditional covariance matrix. An easily estimable RBEKK implies a full albeit constrained BEKK for the unrotated returns. However, the degree of the implied restrictiveness is currently unknown. In this paper, we suggest a Bayesian approach to estimation of the BEKK model with targeting based on Constrained Hamiltonian Monte Carlo (CHMC). We take advantage of suitable parallelization of the problem within CHMC utilizing the newly available computing power of multi-core CPUs and Graphical Processing Units (GPUs) that enables us to deal effectively with the inherent nonlinear constraints posed by covariance targeting in relatively high dimensions. Using parallel CHMC we perform a model comparison in terms of predictive ability of the targeted BEKK with the RBEKK in the context of an application concerning a multivariate dynamic volatility analysis of a Dow Jones Industrial returns portfolio. Although the RBEKK does improve over a diagonal BEKK restriction, it is clearly dominated by the full targeted BEKK model.

Existing multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models either impose strong restrictions on the parameters or do not guarantee a well-defined (positive-definite) covariance matrix. I discuss the main multivariate GARCH models and focus on the BEKK model for which it is shown that the covariance and correlation is not adequately specified under certain conditions. This implies that any analysis of the persistence and the asymmetry of the correlation is potentially inaccurate. I therefore propose a new Flexible Dynamic Correlation (FDC) model that parameterizes the conditional correlation directly and eliminates various shortcomings. Most importantly, the number of exogenous variables in the correlation equation can be flexibly augmented without risking an indefinite covariance matrix. Empirical results of daily and monthly returns of four international stock market indices reveal that correlations exhibit different degrees of persistence and different asymmetric reactions to shocks than variances. In addition, I find that correlations do not always increase with jointly negative shocks implying a justification for international portfolio diversification.

Capital markets thrive on information, and the information revolution has transformed these markets all over the world. Investors can now keep track of the movements of capital markets in real-time and they react to the flow of information from around the world. One of the concerns of stock market investors is whether the markets operate efficiently, independently, and with sound fundamentals. However, real market movements tend to exhibit a link as is evident from recent market movements across the world.

The assessment of interdependence between stock markets is an important aspect of international portfolio management. The aim of this chapter is to examine the shock and volatility spillover between the Standard and Poor’s 500 (S&P500) index from the United States (US) Stock Exchange and the Istanbul Stock Exchange 100 (BIST100) index from the Stock Exchange Istanbul.

S&P500 index, which is the most important index representing US markets, and BIST100 index, which is the index representing the Turkish market, were used as variables in this study. In the analysis, the causality in variance test was applied to determine the volatility spillover between these two markets. Later, multivariate GARCH (MGARCH) models were used to measure the volatility spillover in the markets. VAR(1)-GARCH (1,1)-Diagonal BEKK model was applied to the daily data to determine the shock and volatility spillover in the markets.

As a result of the variance causality test, it was found that there is a bi-directional volatility spillover between S&P500 index and BIST100 index. When the return spillover between the markets is examined, a one-way spillover from the S&P500 index to the BIST100 index emerged. Diagonal BEKK model results show that each market is affected by its own news (unexpected shocks) and volatility. Furthermore, the volatility is persistent for both markets. These findings demonstrate that the US market and the Turkish market interact with each other.

In this paper, we search to evaluate the systemic risk of the Moroccan banking sector. Indeed, we concentrate on the analysis and the evaluation on transverse dimension of the systemic. From this point of view, two approaches were used. First is based on the estimate on value at risk conditional allowing to measure the systemic importance of each banking institution. In addition, the second approach uses the heteroscedasticity models in order to consider the conditional correlations, making it possible, to measure the dependence between the Moroccan banks and with the whole of the financial system. The results obtained with through these two approaches confirm that ATW, BMCI and the BMCE are the most systemic banks in Moroccan banking system and who can initiate a systemic crisis. On another register and by using the conditional correlations of each bank we built an index of systemic risk. Moreover, a macrofinancial model was developed, connecting the index of the systemic risk and the principal macroeconomic variables. This model affirmed that the contagion dimension of systemic risk is procyclical.