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By Peter Grundlke

As a result of their company actions, banks are uncovered to many various possibility kinds. Aggregating numerous chance exposures to a finished probability posistion is a crucial yet up to date no longer satisfactorily solved job. This shortfall is going again to conceptual difficulties of making a suitable possibility version and to the computational burden of opting for a loss distribution that includes all correct possibility forms.

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N } ) are independent of the credit spreads Sη n ( H , Tn ) (η Hn ∈ {1,! , K − 1} ) for all considered maturity dates Tn . H If the issuer n of a zero coupon bond has already defaulted ( η Hn = K ) until the risk horizon H , the value of the bond is set equal to a beta-distributed fraction δ n of the value p ( X r ;( H , Fn , Tn )) of a risk-free, but otherwise identical, zero coupon bond: p( K ; X r ;( H , Fn , Tn , δ n )) = δ n p ( X r ;( H , Fn , Tn )) . 17) Actually, Sη n ( H , Tn ) is the stochastic average credit spread of all obligors in the rating class η Hn .

132). Inhomogeneous exposures: Instead of assuming that the face value of all defaultable zero coupon bonds is identical, a stress test is conducted by assuming that there is one dominating zero coupon bond, whose face value makes up q = 25% of the sum of all face values. With N denoting the number of obligors in the credit portfolio, the face value of the dominating zero coupon bond is chosen as qN and those of the other zero coupon bonds as (1 − q ) N /( N − 1) . Inhomogeneous asset return correlations: To check the sensitivity of the simulation results to the assumption of a homogeneous asset return correlation structure between all pairs of obligors, the case where the portfolio can be decomposed in two groups G1 and G2 of obligor types, which are each homogeneous with respect to their asset return correlation, is considered.

13) = E [ r ( t )] where X r  N (0,1) . 7) of the conditional transition probabilities, credit risk and interest rate risk are dependent in this model. 7): the larger this value is, the higher is the influence of the risk-free interest rates on the asset returns and hence on the conditional transition and default probabilities. As it is assumed in the following that the random variable X r and the systematic credit risk factor Z , respectively, are correlated with the credit spreads, the rating transitions of the obligors, the risk-free interest rates, and the credit spreads are all pairwise correlated in this model.

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