Bounds on total economic capital: the DNB case study
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Most banks use the top-down approach to aggregate their risk types when computing total economic capital. Following this approach, marginal distributions for each risk type are first independently estimated and then merged into a joint model using a copula function. Due to lack of reliable data, banks tend to manually select the copula as well as its parameters. In this paper we assess the model risk related to the choice of a specific copula function. The aim is to compute upper and lower bounds on the total economic capital for the aggregate loss distribution of DNB, the largest Norwegian bank, and the key tool for computing these bounds is the Rearrangement Algorithm introduced in Embrechts et al. (J. Bank. Financ. 37(8):2750–2764 2013). The application of this algorithm to a real situation poses a series of numerical challenges and raises a number of warnings which we illustrate and discuss.
KeywordsModel risk Risk aggregation Total economic capital Value-at-Risk Diversification benefit rearrangement algorithm.
Mathematics Subject Classifications (2010):60E05 91B30
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- Basel Committee on Banking Supervision: International Convergence of Capital Measurement and Capital Standards. Basel: Bank for International Settlements (2004)Google Scholar
- Basel Committee on Banking Supervision: Developments in modelling risk aggregation Basel: Bank for International Settlements (2010)Google Scholar
- Bernard, C., Rüschendorf, L., Vanduffel, S.: Value-at-risk bounds with variance constraints. Preprint, available at SSRN: (2014b). http://ssrn.com/abstract=2342068.
- Brockmann, M., Kalkbrener, M.: On the aggregation of risk. J. Risk 12, 45–68 (2010)Google Scholar
- Cope, E., Mignola, G., Antonini, G., Ugoccioni, R.: Challenges and pitfalls in measuring operational risk from loss data. J. Oper. Risk 4(4), 3–27 (2009)Google Scholar
- Embrechts, P., McNeil, A.J., Straumann, D.: Correlation and dependence in risk management: properties and pitfalls. , In: Risk management: Value at Risk and Beyond, pp 176–223. Cambridge Univ. Press, Cambridge (2002)Google Scholar
- Embrechts, P., Wang, B., Wang, R.: Aggregation-robustness and model uncertainty of regulatory risk measures. Preprint, ETH Zurich (2014)Google Scholar
- Gupton, G.M., Finger, C.C., Bhatia, M.: Creditmetrics. Technical document. (1997)Google Scholar
- Grundke, P.: On the reliability of integrated risk measurement in practice. J. Risk 15(3), 87–110 (2013)Google Scholar
- Hull, J.: Risk Management and Financial Institutions, 3rd edn. Wiley, Hoboken, New Jersey (2012)Google Scholar
- IFRI Foundation and CRO Forum: Insights from the joint IFRI/CRO forum survey on economic capital practice and applications. KPMG Business Advisory Services. (2007)Google Scholar
- McNeil, A.J., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts, Techniques, Tools. Princeton NJ: Princeton University Press (2005)Google Scholar
- Puccetti, G., Wang, R.: General extremal dependence concepts. Preprint, available at SSRN: (2014). http://ssrn.com/abstract=2436392.
- Reitan, T., Aas, K.: A new robust importance-sampling method for measuring value-at-risk and expected shortfall allocation for credit portfolios. J. Credit Risk 6(4), 1–37 (2010)Google Scholar