Abstract
Measuring interdependence between probabilities of default (PDs) in different industry sectors of an economy plays a crucial role in financial stress testing. Thereby, regression approaches may be employed to model the impact of stressed industry sectors as covariates on other response sectors. We identify vine copula based quantile regression as an eligible tool for conducting such stress tests as this method has good robustness properties, takes into account potential nonlinearities of conditional quantile functions and ensures that no quantile crossing effects occur. We illustrate its performance by a data set of sector specific PDs for the German economy. Empirical results are provided for a rough and a fine-grained industry sector classification scheme. Amongst others, we confirm that a stressed automobile industry has a severe impact on the German economy as a whole at different quantile levels whereas, e.g., for a stressed financial sector the impact is rather moderate. Moreover, the vine copula based quantile regression approach is benchmarked against both classical linear quantile regression and expectile regression in order to illustrate its methodological effectiveness in the scenarios evaluated.
Highlights
The stress scenario setup is that we induce stress on a single industry sector and evaluate how this affects the other sectors by employing D-vine copula based quantile regression
We apply what is referred to as extremal quantile regression (QR) in the introduction and this yields the intuitive interpretation that the covariate is stressed to 95% or 99%
In order to motivate the use of D-vine copula based quantile regression in our stress test, we would like to point out methodological alternatives and discuss the advantages and shortcomings of the different approaches
Summary
Stress testing identifies potential vulnerabilities of financial institutions under hypothetical or historical scenarios. The primary interest lies in the explanation (in a first step) and the initiation of stress (in a second step) of the counterparties’ In this context, quantile regression (QR) is an increasingly important empirical tool in economics and other sciences for analyzing the impact a set of regressors (e.g., macro-economic variables) has on the conditional distribution of an outcome (here: PD). We circumvent the disadvantages of classical QR, namely the occurrence of so-called quantile-crossings and apply D-vine copula based quantile regression as recently advocated by Kraus and Czado (2017a), instead. Against this background, the outline of this work is as follows: Section 2 briefly reviews.
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