CAViaR models for Value at Risk and Expected Shortfall with long range dependency features
Abstract
We consider alternative specifications of conditional autoregressive quantile models to estimate Value-at-Risk (VaR) and Expected Shortfall (ES). The proposed specifications include a slow moving component in the quantile process, along with aggregate returns from heterogeneous horizons as regressors. Using data for ten stock indices over a period that incorporated the global financial crisis, we evaluate the performance of the models and find that the proposed features are useful in capturing tail dynamics better.