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Application of the Merton model to estimate the probability of breaching the capital requirements under Basel III rules


In this paper, we estimate the probability of a financial institution breaching the Common Equity Tier 1 capital under Basel III rules. We do so by applying the Merton model, where balance sheet data and market data are used to match the probability of default implied by the model with the probability of default implied by market quotations for credit default swaps. We provide an empirical analysis for several banks classified by the Financial Stability Board and the Basel Committee on Banking Supervision as Global Systemically Important Financial Institutions, evaluating how the probability of breaching the Common Equity Tier 1 Capital evolved from 2005 to 2015. We find that higher Common Equity Tier 1 Capital ratios do not necessarily imply lower probabilities of breaching capital requirements and vice versa. We also focus on the asset volatility calibrated according to our model and we find that it appears to be a good proxy for the risk-weighted asset density.

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  1. Using the discretion allowed for by the Basel II framework and specifically of the internal rating-based approach, banks calculate capital requirements that are typically lower than the requirements obtained under the standard approach. (Barucci and Milani 2018; Vallascas and Hagendorff 2013).

  2. As specified in BCBS (2011), minimum Common Equity Tier 1 Capital “consists of the sum of the following elements: Common shares issued by the bank that meet the criteria for classification as common shares for regulatory purposes (or the equivalent for non-joint stock companies); Stock surplus (share premium) resulting from the issue of instruments included Common Equity Tier 1; Retained earnings; Accumulated other comprehensive income and other disclosed reserves; Common shares issued by consolidated subsidiaries of the bank and held by third parties (i.e. minority interest) that meet the criteria for inclusion in Common Equity Tier 1 capital; and Regulatory adjustments applied in the calculation of Common Equity Tier 1”. For the years 2013 and 2014 the minimum ratio was 3.5% and 4.0%, respectively.

  3. The minimum ratio according to BCBS (2011) was 8.0% in 2014, 8.625% in 2016, and 9.25% in 2017. For 2018 and 2019 this ratio is expected to be 9.875% and 10.5% respectively.

  4. According to the BCBS (2011), regulatory capital consists of (i) Core capital (basic equity or Tier 1 Capital, which can be considered as the going-concern capital)—made of Common Equity Tier 1 and Additional Tier 1, and (ii) Supplementary capital (or Tier 2, which is the gone-concern capital). In addition to these elements, the BCBS requires: (iii) a capital conservation buffer (which is designed to ensure that banks build up capital buffers outside periods of stress which can be drawn down as losses are incurred. The requirement is based on simple capital conservation rules designed to avoid breaches of minimum capital requirements) and a (iv) countercyclical buffer that aims to ensure that banking sector capital requirements take account of the macro-financial environment in which banks operate.

  5. The banks selected are those for which market data are available to be used as input for the proposed model.

  6. See Black and Scholes (1973) and Merton (1974).

  7. A widely used approach to calibrate Merton’s model has been proposed by Crosbie and Bohn (2002).

  8. See Liberadzki and Liberadzki (2019) for further details on these topics.

  9. We apply the standard bootstrapping technique to derive the spot rates from the traded market instruments.

  10. CDSs with a 5-year maturity were considered for the analysis because they were the most liquid tenors.


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Correspondence to Marina Brogi.

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Russo, V., Lagasio, V., Brogi, M. et al. Application of the Merton model to estimate the probability of breaching the capital requirements under Basel III rules. Ann Finance 16, 141–157 (2020).

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  • Probability of breaching
  • Basel III rules
  • Merton model
  • Credit default swap
  • Global Systemically Important Financial Institutions

JEL Classification

  • G21
  • G28