Asymmetric CAPM dependence for large dimensions: the Canonical Vine Autoregressive Model

We propose a new dynamic model for volatility and dependence in high dimensions, that allows for departures from the normal distribution, both in the marginals and in the dependence. The dependence is modeled with a dynamic canonical vine copula, which can be decomposed into a cascade of bivariate conditional copulas. Due to this decomposition, the model does not suffer from the curse of dimensionality. The canonical vine autoregressive (CAVA) captures asymmetries in the dependence structure. The model is applied to 95 S&P500 stocks. For the marginal distributions, we use non-Gaussian GARCH models, that are designed to capture skewness and kurtosis. By conditioning on the market index and on sector indexes, the dependence structure is much simplified and the model can be considered as a non-linear version of the CAPM or of a market model with sector effects. The model is shown to deliver good forecasts of Value-at-Risk.asymmetric dependence, high dimension, multivariate copula, multivariate GARCH, Value-at-Risk

A partial correlation vine based approach for modeling and forecasting multivariate volatility time-series

A novel approach for dynamic modeling and forecasting of realized covariance matrices is proposed. Realized variances and realized correlation matrices are jointly estimated. The one-to-one relationship between a positive definite correlation matrix and its associated set of partial correlations corresponding to any vine specification is used for data transformation. The model components therefore are realized variances as well as realized standard and partial correlations corresponding to a daily log-return series. As such, they have a clear practical interpretation. A method to select a regular vine structure, which allows for parsimonious time-series and dependence modeling of the model components, is introduced. Being algebraically independent the latter do not underlie any algebraic constraint. The proposed model approach is outlined in detail and motivated along with a real data example on six highly liquid stocks. The forecasting performance is evaluated both with respect to statistical precision and in the context of portfolio optimization. Comparisons with Cholesky decomposition based benchmark models support the excellent prediction ability of the proposed model approach

Modeling the Dependence Structure of the WIG20 Portfolio Using a Pair-copula Construction

Elliptical distributions commonly applied to modeling the returns of stocks in high-dimensional portfolio are not capable of adequate describing the dependence between the components when their statistical properties are very diverse. The MGARCH and standard dynamic copula models are often of little usefulness in such cases. In this paper, we apply a methodology called the pair-copula decomposition to model the joint conditional distribution of the returns on stocks constituting the WIG20 index, and show some advantage of this construction over the approach using the t Student DCC model.dependence, portfolio, copula, pair-copula construction.

Modeling International Financial Returns with a Multivariate Regime Switching Copula

In order to capture observed asymmetric dependence in international financial returns, we construct a multivariate regime-switching model of copulas. We model dependence with one Gaussian and one canonical vine copula regime. Canonical vines are constructed from bivariate conditional copulas and provide a very flexible way of characterizing dependence in multivariate settings. We apply the model to returns from the G5 and Latin American regions, and document two main findings. First, we discover that models with canonical vines generally dominate alternative dependence structures. Second, the choice of copula is important for risk management, because it modifies the Value at Risk (VaR) of international portfolio returns.Asymmetric dependence; Canonical vine copula; International returns; Regime-Switching; Risk Management; Value-at-Risk

Modeling international financial returns with a multivariate regime switching copula

In order to capture observed asymmetric dependence in international financial returns, we construct a multivariate regime-switching model of copulas. We model dependence with one Gaussian and one canonical vine copula regime. Canonical vines are constructed from bivariate conditional copulas and provide a very flexible way of characterizing dependence in multivariate settings. We apply the model to returns from the G5 and Latin American regions, and document two main findings. First, we discover that models with canonical vines generally dominate alternative dependence structures. Second, the choice of copula is important for risk management, because it modifies the Value at Risk (VaR) of international portfolio returns.asymmetric dependence, canonical vine copula, international returns, regime-switching, risk management, Value-at-Risk.

Modelling international financial returns with a multivariate regime switching copula

In order to capture observed asymmetric dependence in international financial returns, we construct a multivariate regime-switching model of copula. We model dependence with one Gaussian and one canonical vine copula regime. Canonical vines are construted from bivariate conditional copulas and provide a very flexible way of characterizig dependence in multivariate settings. We apply the model to returns from the G5 and Latin American regions, and document two main findings. First, we discover that models with canonical vines generally dominate alternative dependence structures. Second, the choice of copula is important for risk management, because it modifies the Value at Risk (VaR) of international portfolio returns.asymmetric dependence, canonical vine copula, international returns, regime-switching, risk management, Value-at-Risk