A copula-based systemic risk measure: application to investment-grade and high-yield CDS portfolios

ABSTRACT

This study investigates the evolution of systemic risk inherent in investment-grade (IG) and high-yield (HY) CDS portfolios and compares the portfolios before and after the global financial crisis. To quantify systemic risk, we propose a novel measure – the expected default rate (EDR), defined by the average default rate of all institutions conditional upon one institution being in default. We implement the EDR under the one-factor copula framework with various dependence structures. We observe that the HY portfolio contains a higher systemic risk than the IG’s, overall, and the gap between the two widens after Lehman Brothers’ default. However, the model discrepancy for IG EDR is higher than that for HY, and for both the IG and HY EDRs, the discrepancies decrease over time.

KEYWORDS:

• Systemic risk measure
• copula
• expected default rate
• IG and HY CDS portfolios

JEL CLASSIFICATION:

• C51
• C59
• G33

Acknowledgments

We are grateful to an anonymous reviewer for helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ For the double-$t$ copula, since $F_{X_i}$ is not expressed as a specific distribution, this paper calculates it using the Gauss-Legendre quadrature, and then finds $F_{X_i}^{-1}$ by a root-finding algorithm (see Vrins 2009).

² We exclude the on-the-run series during the period from 4Q 2008 to 2009 due to the significant lack of missing data. As an alternative, we choose the 7-year maturity of an earlier series. With the same reason, we exclude senior tranches with a detachment point exceeding 15% level.

³ https://lauder.wharton.upenn.edu/wp-content/uploads/2015/06/Chronology_Economic_Financial_Crisis.pdf.

Additional information

Funding

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT [NRF-2019R1H1A2039709] and by “Human Resources Program in Energy Technology’’ of the Korea Institute of Energy Technology Evaluation and Planning (KETEP); granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea [no. 20184010201680].