Determining marginal contributions of the economic capital of credit risk portfolio: an analytical approach

Morone, Marco and Cornaglia, Anna and Mignola, Giulio (2012): Determining marginal contributions of the economic capital of credit risk portfolio: an analytical approach.

Abstract

We address the problem of decomposing the risk of a multi-factor credit portfolio into marginal contributions through a fast analytical approach: it is based on Taylor polynomial expansion of the overall risk and on the subsequent partial derivatives with respect to the single exposures, exploiting the Euler principle. The proposed approximation, which also accommodates for an efficient treatment of obligors with similar risk profile, is suitable for large and complex bank portfolios; furthermore, it proves to perform quite well if tested against numerical techniques, among which we chose the Harrel-Davis estimator. The latter, aside from representing a benchmark measure, should however be applied in the case of very small and concentrated portfolios. In addition, a comparison with the most usual variance-covariance approach is drawn, emphasising its drawbacks in the correct representation of risk allocation.

• Item Type: MPRA Paper
• Language: English
• Keywords: Credit VaR; Portfolio credit risk; Economic capital; Analytical VaR contributions; Euler allocation; Harrel-Davis estimator
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; G - Financial Economics > G3 - Corporate Finance and Governance > G32 - Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill

References

Dullmann K., Puzanova, N. (2011). Systemic Risk Contributions: A Credit Portfolio Approach. Deutsche Bundesbank, Discussion Paper 8.

Emmer, S., Tasche, D., (2003). Calculating Credit Risk Capital Charges with the One-Factor Model. Working Paper.

Gouriéroux, C., Laurent, J. P. and Scaillet, O. (2000). Sensitivity analysis of values at risk. Journal of Empirical Finance 7, 225-245.

Gordy, M. B. (2003). A risk-factor model foundation for ratings-based bank capital rules. Journal of Financial Intermediation 12, 199-232.

Hibbeln, M. (2010). Risk Management in Credit Portfolios. Concentration Risk and Basel II. Physica-Verlag.

Harrell, F., Davis, C. (1982). A new distribution-free quantile estimator. Biometrika 69 (3), 635–640.

Kalkbrener, M., Lotter, H., Overbeck, L. (2004). Sensible and efficient capital allocation for credit portfolios. Risk (January), 19-24.

Lutz, H., When, C. (2012). Analytical risk contributions for non-linear portfolios. Risk Magazine (January), 41-44.

Mausser, H. (2003). Calculating quantile-based risk analytics with L-estimators. Journal of Risk Finance 4 (3), 61–74.

Mausser, H., Rosen, D. (2008). Economic Credit Capital Allocation and Risk Contributions. Handbooks in OR & MS vol.15, 681-726.

Pykhtin, M. (2004). Multi-factor adjustment. Risk Magazine, 85-90.

Tasche, D. (2007). Euler Allocation: Theory and Practice. Working paper.