On modeling financial risk with tail copulas

Abstract

This thesis is a cumulative one, comprising three peer-reviewed and published papers. The first article studies, for the first time in the literature, the dependence of extreme events in energy markets. It is shown that adopting general copula inference techniques (applying a goodness-of-fit test for copulas to the whole support of the bivariate distribution) can be very misleading for modeling the joint tail behavior. Moreover, the advantage of tail copulas over the single tail dependence coefficients is emphasized. The objective of the second article is the modeling of stochastic tail dependence in energy and commodity markets. The essential part is the application of a newly introduced partial derivatives multiplier bootstrap goodness-of-fit test for tail copulas. The findings are then compared to a traditional copula fit. Finally, the article provides a comprehensive backtesting framework for the risk measures Value-at-Risk and Expected Shortfall. As suspected, the best tail copula model slightly outperforms the traditional copula fit. The third article develops asymptotic tests for detecting structural breaks in the tail dependence of multivariate time series. In particular, to obtain asymptotic properties, a new limit result for the sequential empirical tail copula process is derived. Moreover, an elaborated simulation study investigates the finite sample properties of the proposed testing procedures. In the observed behavior, the tests are slightly conservative combined with reasonable power properties. The study further reveals that the asymptotic behavior of the estimator based on time series residuals is the same as the one based on independent and identically distributed observations.