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 departuresfrom the normal distribution, both in the marginals and in the dependence. The dependence is modeled with adynamic canonical vine copula, which can be decomposed into a cascade of bivariate conditional copulas. Dueto this decomposition, the model does not suffer from the curse of dimensionality. The canonical vineautoregressive (CAVA) captures asymmetries in the dependence structure. The model is applied to 95 S&P500stocks. For the marginal distributions, we use non-Gaussian GARCH models, that are designed to captureskewness and kurtosis. By conditioning on the market index and on sector indexes, the dependence structure ismuch simplified and the model can be considered as a non-linear version of the CAPM or of a market modelwith sector effects. The model is shown to deliver good forecasts of Value-at-Risk.....