Zusammenfassung |
In the last years the quantitative modelling of credit risk has received a lot of attention within the financial industry. Several models have been released to the public, notably CreditRisk+, Credit Metrics, Credit Portfolio View [CR97, CM97, CP98]. Although different approaches to credit risk are used, studies have shown that the models yield similar results if the parameters are set in a consistent way, see for example [KO98]. CreditRisk+ in particular is ideal for practical implementation and has some nice features, namely: (a) few assumptions have to made, (b) the methodology is very transparent and based on concepts already used in the insurance business, and (c) the loss distribution can be calculated analytically in an efficient way using an iterative procedure. One of the shortcomings of the CreditRisk+ model is the assumption of independent sectors. The sectors represent for example different regions or industries within the economy and individual onligors can be assigned to particular sectors. In order to perform a sector analysis, the authors of CreditRisk+ propose apportioning an obligor's systematic risk across a mixture of independent sectors. However, such an approach is difficult to realize in practice. In this paper, we present a framework for extending the CreditRisk+ model by examining correlations between industries and derive a formula for the unexpected loss and risk contributions. The correct modelling of correlations of default risk between sectors is very important for examining the effects of diversification on active portfolio management. Note that only the loss from defaults of counterparties is modelled. The article is organized as follows: we first derive the probability generating function of the loss distribution for one sector following the CreditRisk+ approach. This is then generalized to several sectors to obtain the first two moments of the loss distribution, as well as a loss distribution consistent wiith the observed correlations between sectors. |