Three PD-LGD models for a stress test exercise

Abstract

In response to the financial instability that has grown over the past 30 years, policymakers have proposed methodologies for understanding, quantifying and monitoring the vulnerabilities of financial systems and measures that could help prevent financial crises. In this context, the Basel framework has evolved steadily over the 2010s to help the banking system manage its credit risks by conducting stress-testing exercises under an increasing number of adverse scenarios such as climate change, high inflation, geopolitical tensions or pandemics. Some financial institutions have developed their own internal methodologies to assess the capital requirement that best corresponds to their exposure to adverse risks. However, one challenging aspect of the issue is frequently neglected: the modelling of the Loss Given Default. It is now widely recognized that the LGD is sensitive to economic conditions and should therefore be modeled in the same way as the Probability of Default, with sensitivity to scenarios. But it can be difficult to obtain high-quality data and explain it using the standard macro-financial variables commonly used in stress-testing exercises. In this paper, we propose a simple approach to include a modelled LGD as part of a stress test using the PD-LGD dependency. We study three PD-LGD models and obtain an assessment of capital requirements that depends only on the PD, hence simple to use for banks. We illustrate our approach by conducting a carbon price stress test on the Stoxx 600 index.

Keywords: Probability of default, loss given default, stress test, PD-LGD dependency

JEL Classification: E22, E47, G32, Q54