Pricing the Risks of Default: A Note on Madan and Unal

In their well-known article, Madan and Unal (1998) presented one of the first intensity-based credit risk models. In this approach the default intensity is directly linked to the market value of the firm's equity. In order to derive the probability of default Madan and Unal have to solve a partial differential equation (PDE). Here, we show that one of the transformations in the derivation of the solution of this PDE is not correct and analyze the difference between the correct solution of the PDE and the solution based on the incorrect transformation. As a consequence of the transformation error the credit risk of a debtor is systematically underestimated.     

Model and estimation risk in credit risk stress tests

Review of Quantitative Finance and Accounting - This paper deals with stress tests for credit risk and shows how exploiting the discretion when setting up and implementing a model can drive the...     

A macroeconomic reverse stress test

Reverse stress tests are a relatively new stress test instrument that aims at finding exactly those scenarios that cause a bank to cross the frontier between survival and default. Afterward, the scenario which is most probable has to be identified. This paper sketches a framework for a quantitative reverse stress test for maturity-transforming banks that are exposed to credit and interest rate risk and demonstrates how the model can be calibrated empirically. The main features of the proposed framework are: (1) the necessary steps of a reverse stress test (solving an inversion problem and computing the scenario probabilities) can be performed within one model, (2) scenarios are characterized by realizations of macroeconomic risk factors, (3) principal component analysis helps to reduce the dimensionality of the space of systematic risk factors, (4) due to data limitations, the results of reverse stress tests are exposed to considerable model and estimation risk, which makes numerous robustness checks necessary.     

Global systemic risk measures and their forecasting power for systemic events

Since the financial crisis of 2007–2009, many market-based systemic risk measures have been proposed. Prominent examples are MES, SRISK or ΔCoVaR. Based on a simulation study in an extended banking network model that incorporates several sources of systemic risk, we analyze how well these systemic risk measures perform in indicating the risk of a systemic event. For this analysis, the systemic risk measures of the banks that default and whose default is followed by a systemic event are compared with the systemic risk measures of those defaulting banks for which no subsequent systemic event can be observed. Within the simulation study, we find that many bank-individual systemic risk measures are statistically significant in explaining the likelihood of a systemic event after a bank’s default. However, the economic significance of the bank-individual systemic risk measures is relatively low.     

Ranking consistency of systemic risk measures: a simulation-based analysis in a banking network model

Review of Quantitative Finance and Accounting - In a banking network model, I analyse the ranking consistency of common systemic risk measures (SRMs). In contrast to previous studies, this...