yvonne kreis. systemic risk in a structural model of bank default linkages

Eesti Pank – August 2016 © 2016 Kreis

Systemic Risk in a Structural Model of Bank Default Linkages

Yvonne KreisGutenberg University Mainz

Dietmar LeisenGutenberg University Mainz


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This Paper• Structural model of bank default in an asset-

based approach

• Focus on the impact of asset correlations

• Systemic risk measure: Conditional Expected Default Frequency

• Empirical analysis for the U.S. banking sector:

• Macro-prudential regulation required; SIFI capital supplement too “small”


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AgendaMotivationModelCorrelationImplications & RegulationConclusion


Motivation I: Level of Interconnectedness• Banks are interconnected on several layers.

– Direct connection (asset investments, loans)– Indirect connection via common (systemic)

factors (e.g. market risk perception)• Severe systemic events affect all banks

through direct and / or indirect connections. (e.g. exposure, risk perception, trust in and between banks)

• Current literature often focuses on modeling direct connections.

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Motivation II: Impact of Systemic Risk

• Severe systemic events affect all banks.

• Only relevant factor during a financial crises

• Single Factor Approach to Systemic Risk

• Foundation: Vasicek (1987)

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Motivation III: Default

• Default results from the balance sheet.

• Regulation focuses on assets.

• Asset Based Approach to Systemic Risk

• Foundation: Structural Model by Merton (1974)

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Structural Model of Default• Individual bank defaults iff assets < debt

<

• Introduce default correlation through asset correlation

V = +

• Study a banking system with N individual banks

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Normal Periods vs. Crisis Periods• Normal periods

encompasses fundamental factors, e.g. KMV.

• Crisis periods

encompasses only the systemic shock.

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= , + , ,

= , + , ,


Default Frequency • Individual default probability • Indicator variable for default of bank i: Xi

• Default frequency: =

• Conditional default probability

• Conditional distribution of default frequency

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Density of Default Frequency MN

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parameters: p=1%; N=1,000


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Data• Analyses for the U.S. banking sector 1980 – 2015

• Selection of “core” sector, i.e. 15 large banks

• Daily stock price returns as approximation of asset returns

• Application of a principal component analysis– over a rolling 3-month window– mean (median) factor loadings of the first

principal component

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Time Series of Average Correlation14


Time Series of Average Correlation 15


Asset Correlations• Asset correlations between banks have strongly

increased over time!

• They have become very high in the past decade!

• This strongly influences the bank default linkages and thus systemic risk!

• How to adequately introduce to risk management?

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Risk Measures• For correlation=0, Law of Large Numbers implies

– suggests that default frequency is close to individual default probability (micro-prudential regulation)

• Actual numbers are far too small to capture “infinity”.

• Need to capture departure from p– Study Conditional Expected Default Frequency:

= [ | ]– foundation for macro-prudential regulation

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Conditional Expected Default Frequency19


U.S. Sample: Temporal Evolution of CEDF20


Outlook: Relative Systemic Capital Supplement on Correlation

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Conclusion• Approach to systemic risk based on well-known

structural model to credit risk

• Asset correlations have a strong impact (shape of the density of default frequencies, risk measure, and thus capital requirements)

• “Large” correlation levels imply that stronger macro-prudential regulation is required

• Next steps: stress testing & systemic capital

yvonne kreis. systemic risk in a structural model of bank default linkages

Economy & Finance