Single index based CoVaR with very high dimensional covariates

Systemic risk analysis reveals the interdependencies of risk factors especially in tail event situations. In applications the focus of interest is on capturing joint tail behavior rather than a variation around the mean. Quantile and expectile regression are used here as tools of data analysis. When it comes to characterizing tail event curves one faces a dimensionality problem, which is important for CoVaR (Conditional Value at Risk) determination. A projection based single index model specification may come to the rescue but for ultra high dimensional regressors one faces yet another dimensionality problem and needs to balance precision vs. dimension. Such a balance is achieved by combining semi parametric ideas with variable selection techniques. In particular, we propose a projection based single index model specification for very high dimensional regressors. This model is used for practical CoVaR estimates with a systemically chosen indicator. In simulations we demonstrate the practical side of the semiparametric CoVaR method. The application to the US financial sector shows good backtesting results and indicate market coagulation before the crisis period.