Title: Clustering Extreme Value Indices in Large Panels
Abstract: We analyze a large panel of units grouped by shared extreme value indices (EVIs) and aim to identify these unknown groups. To achieve this, we order the Hill estimates of individual EVIs and segment them by minimizing the total squared distance between each estimate and its corresponding group average. We show that our method consistently recovers group memberships, and we establish the asymptotic normality of the proposed group estimator. The group estimator attains a faster convergence rate than the individual Hill estimator, leading to improved estimation accuracy. Simulation results reveal that our method achieves high empirical segmentation accuracy, and the resulting group EVI estimates substantially reduce mean absolute errors compared to individual estimates. We apply the proposed method to analyze a rainfall dataset collected from 4,735 stations across Europe, covering the winter seasons from January 1, 1950, to December 31, 2020, and find statistically significant evidence of an increase in the highest and a decrease in the lowest group EVI estimates, suggesting growing variability and intensification of extreme rainfall events across Europe.
This talk is based on a joint work with Juan-Juan Cai, Yicong Lin and Julia Schaumburg.
Title: Systemic Risk – CoVaR, Comovement and Portfolio Selection
Abstract: Systemic risk concerns the impact of an individual entity on a financial system, while (extreme) comovement measures one individual (extreme) loss given another individual (extreme) loss. A natural and challenging question is how to measure and forecast the collective impact of two individual losses on systemic risk, conditional on certain predictors and the comovement of these two individuals. In this paper, we introduce a novel systemic risk measure, CoVaRCM, which integrates both comovement and predictor variables to assess the joint effect of two individual losses on systemic risk. Since the comovement event in our model depends on predictors and has zero probability, we employ a three-quantile regression model to conduct an efficient inference. We further propose two metrics to compare CoVaRCM with the more conventional CoVaR. Our empirical analysis demonstrates the significant influence of comovement on systemic risk. We also discuss a statistical inference for systemic risk-driven portofolio selection.