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Quantifying the impact of different copulas in a generalized CreditRisk$$^+$$ framework. An empirical study. (English) Zbl 1292.91181
Summary: Without any doubt, credit risk is one of the most important risk types in the classical banking industry. Consequently, banks are required by supervisory audits to allocate economic capital to cover unexpected future credit losses. Typically, the amount of economical capital is determined with a credit portfolio model, e.g. using the popular CreditRisk$$^+$$ framework (1997) or one of its recent generalizations. Relying on specific distributional assumptions, the credit loss distribution of the CreditRisk$$^+$$ class can be determined analytically and in real time. With respect to the current regulatory requirements, banks are also required to quantify how sensitive their models (and the resulting risk figures) are if fundamental assumptions are modified. Against this background, we focus on the impact of different dependence structures (between the counterparties of the bank’s portfolio) within a (generalized) CreditRisk$$^+$$ framework which can be represented in terms of copulas. Concretely, we present some results on the unknown (implicit) copula of generalized CreditRisk$$^+$$ models and quantify the effect of the choice of the copula (between economic sectors) on the risk figures for a hypothetical loan portfolio and a variety of parametric copulas.

##### MSC:
 91G40 Credit risk 91G10 Portfolio theory 62P05 Applications of statistics to actuarial sciences and financial mathematics 62H30 Classification and discrimination; cluster analysis (statistical aspects)
##### Software:
copula; copula; CRAN; CreditRisk+; ghyp; HAC
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##### References:
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