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BSLoss - A Comprehensive Measure for Interconnectedness

Core Content

The paper introduces BSLoss (Banking System Loss) as a novel measure to quantify the contagion risks within the banking system. It is designed to capture the negative externalities caused by interconnectedness and assess the systemic importance of individual banks. The methodology is based on the DebtRank framework proposed by Battiston et al. (2012), which evaluates the central role of banks in financial networks.

Main Objectives and Research Questions

• Quantify negative externalities from interconnectedness in the banking system.
• Evaluate the effectiveness of different policy actions, such as capital buffers, in mitigating contagion risks.
• Rank banks based on their systemic importance, considering both direct and indirect contagion effects.

Key Features of BSLoss

• Reflects aggregated credit losses in the banking system initiated by an exogenous shock.
• Accounts for both direct and indirect contagion effects.
• Captures the feedback loop between credit quality, capital ratios, and risk-weighted assets.
• Forward-looking and market value-based, making it economically meaningful.

Algorithm Overview

The algorithm simulates the contagion process in a multi-round manner:

1. Initial shock: An exogenous increase in the Probability of Default (PD) of certain banks.
2. Propagation mechanism:
   • The Tier1 capital ratio of creditor banks is updated based on the loss given default (LGD) and the credit exposure from debtor banks.
   • The risk-weighted assets (RWA) of each bank are updated using the IRB formula.
   • The PD of each bank is then updated based on the Tier1 capital ratio and logit-regression analysis.
3. Termination: The process stops when the change in PD is less than a small threshold (ε > 0).

Ranking of Banks

• BSLossT1 represents the total loss in the banking system.
• BSLossDir captures the direct contagion effect from the initial shock.
• BSLossInd represents the indirect contagion effect.
• % defaultsT indicates the percentage of banks that default in the final round.

Methodology

• Propagation mechanism:
  • Tier1 capital ratio and RWA are updated in each round based on the PD changes of debtor banks.
  • The PD of a bank is updated using a logit-regression model, which relates Tier1 capital ratio to PD.
• Empirical relationship:
  • The logit-regression model is used to estimate the PD based on capital ratios and control variables (CAMEL ratings).
• IRB formula:
  • Risk weights (RW) are calculated using the Internal Ratings-Based (IRB) approach, which depends on PD, LGD, and maturity (M).
  • The asset correlation (ρ) is defined as a function of PD.

Policy Implications

• Capital buffers are evaluated for their ability to absorb shocks.
• The BSLoss metric can be used to identify systemically important banks and assess the effectiveness of regulatory interventions.

Conclusion and Extensions

• BSLoss provides an analytical framework for quantifying contagion risks in the banking system.
• It helps in identifying "too-interconnected-to-fail" banks and evaluating policy responses.
• Future extensions include:
  • Incorporating non-bank financial institutions (e.g., insurers).
  • Comparing financial systems across countries and conducting dynamic analyses.
  • Using unconditional BSLoss, weighted by rating downgrade probabilities of the shocked banks.

References

• Allen, F., & Gale, D. (2000). Financial Contagion. The Journal of Political Economy.
• Battiston, S., et al. (2012). Debtrank: Too central to fail? Financial networks, the fed and systemic risk. Scientific Reports.
• Bonacich, P., & Lloyd, P. (2001). Eigenvector-like measures of centrality for asymmetric relations. Social Networks.
• Craig, B., Kotter, M., & Krüger, U. (2014). Interbank Lending and Distress: Observables, Unobservables, and Network Structure. Discussion Paper, Deutsche Bundesbank.
• Eisenberg, L., & Noe, T. H. (2001). Systemic Risk in Financial Systems. Management Science.