We test the naive model to forecast ex-ante Value-at-Risk (VaR) using a shrinkage estimator between realized volatility estimated on past return time series, and implied volatility quoted on the market. Implied volatility is often indicated as the operators expectation about future risk, while...

We consider VAR models for variables exhibiting cointegration and comon cyclical features. While the presence of cointegration reduces the rank of the long-run multiplier matrix, other types of common features lead to rank reduction of the short-run dynamics. We distinguish between strong and...