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Determining Marginal Contributions of the Economic Capital of Credit Risk Portfolio: An analytical approach

by Marco Morone of Intesa Sanpaolo,
Anna Cornaglia of Intesa Sanpaolo, and
Giulio Mignola of Intesa Sanpaolo

June 2012

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.

JEL Classification: C15, G32.

AMS Classification: 91G40, 68W25, 65C05.

Keywords: Credit VaR, Portfolio credit risk, Economic capital, Analytical VaR contributions, Marginal contributions, Euler allocation, Harrel-Davis estimator.

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