# Stress Testing German Industry Sectors: Results from a Vine Copula Based Quantile Regression

## TL;DR

This paper introduces a vine copula-based quantile regression method for stress testing industry sectors, demonstrating its robustness and ability to model nonlinear dependencies in German PD data, with significant implications for financial risk assessment.

## Contribution

It presents a novel application of vine copula-based quantile regression for stress testing, highlighting its advantages over traditional methods in capturing complex sector interdependencies.

## Key findings

- Stressed automobile sector significantly impacts the German economy.
- Vine copula quantile regression outperforms classical linear and expectile regression.
- Method demonstrates robustness and handles nonlinearities effectively.

## 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.