Multivariate Risk: From Univariate to High-Dimensional Graphical Models

Abstract: We present a comparison of different univariate and multivariate extreme value risk models. Our focus is on exploring how these can be used to model financial risk. We use simulated as well as real data and compare deterministic and cross-validation threshold selection methods for the GP model to a GEV model. For comparison, we carry out a bivariate analysis using copulas. Finally, an undirected graphical lasso model using n=45 block maxima of the log-returns from 95 of the stocks in the FTSE 100 index is combined with copulas and PCA to model the extreme loss risk within the FTSE 100 index. The contribution of this study lies in exploring some ideas on risk models in multivariate high-dimensional settings.