Abstract
The Basel Committee on Banking Supervision sets the official confidence level at which a bank is supposed to absorb annual losses at 99.9 per cent. However, due to an inconsistency between the notion of expected losses in the Vasicek model, on the one hand, and the practice of Basel regulation, on the other hand, actual confidence levels are likely to be lower. This article calculates the minimal confidence levels that correspond to a worst case scenario in which a Basel-regulated bank holds capital against unexpected losses only. I argue that the probability of a bank failure is significantly higher than the official 0.1 per cent if, firstly, the bank holds risky loans and if, secondly, the bank was previously affected by substantial write-offs.
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Notes
I equivalently refer to a bank's portfolio value as the bank's total exposure at default.
Note that this list of implicit or explicit assumptions of the Basel VaR approach might not be complete. For example, in Da-Rocha Lopes, S. and Nunes, T. (2010) A simulation study on the impact of correlation between LGD and EAD on loss calculation when different LGD definitions are considered. Journal of Banking Regulation 11(2): 156–167, it is pointed out that the implicit Basel VaR assumption, according to which LGD and EAD are uncorrelated, might be violated in practice.
Throughout the article I neglect the Basel firm size adjustment according to which the correlation between small firms is (slightly) lower than the correlation between large firms. I also simplify the original Basel definition
because, for all practical purposes, exp(−50)=0.
Fix π(default) and observe that
is strictly decreasing in q. To determine q* in (61) it is therefore sufficient to find the root q* of the univariate nonlinear equation
I solve this using Brent's method (cf., for example, Judd, K. (1999) Numerical Methods in Economics. Cambridge, MA: MIT Press, The Matlab code is provided at http://www.sfb504.uni-mannheim.de/126zimper/solveq.m.
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Acknowledgements
I would like to thank Davy Corubolo, Guangling (Dave) Liu, an anonymous referee and the editor Dal Singh for helpful comments and suggestions. I am grateful to Alex Ludwig for helping me with the Matlab code.
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Appendix
Appendix
NUMERICAL VALUES FOR q*
The following table lists minimal confidence level values for selected default probabilities.
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Zimper, A. The minimal confidence levels of Basel capital regulation. J Bank Regul 15, 129–143 (2014). https://doi.org/10.1057/jbr.2013.5
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DOI: https://doi.org/10.1057/jbr.2013.5