In the short time since their public releases in 1997, J.P. Morgan's CreditMetrics and Credit Suisse's CreditRisk have become in uential benchmarks for internal credit risk models. Practitioners and policy makers have invested in implementing and exploring each of the models individually, but have made less progress with comparative analyses. Direct comparison of the models is not straightforwa...

Capital allocation for credit portfolios has two meanings. First, at portfolio level it means to determine capital as a buffer against an unexpected negative cash-flow resulting from credit losses. In this case, the allocation method can be specified by means of a risk measure. Its result is called economic capital of the portfolio. Second, at sub-portfolio or transaction level, capital allocat...

Introduction In the last few 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+, CreditMetrics, 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 ...

This paper presents analytical solutions to the problem of how to calculate sensible VaR (Value-at-Risk) and ES (Expected Shortfall) contributions in the CreditRisk+ methodology. Via the ES contributions, ES itself can be exactly computed in finitely many steps. The methods are illustrated by numerical examples.

CreditRisk+ is an influential and widely implemented model of portfolio credit risk. As a close variant of models long used for insurance risk, it retains the analytical tractability for which the insurance models were designed. Value-at-risk can be obtained via a recurrence-rule algorithm, so Monte Carlo simulation can be avoided. Little recognized, however, is that the algorithm is fragile. U...

We discuss the CreditRisk+ methodology from the perspective of the moment generating function of the credit factors. This representation lends itself to a new recursion formula for the portfolio loss distribution that is more accurate and considerably faster, particularly for large portfolios. We discuss how the model can be extended to incorporate correlations between risk factors and derive t...

The default risk of firms is driven by firm-specific factors but also by systematic factors and the latter are responsible for default dependence between different firms. Another source of default dependence is structural links between firms. For example, a mother company may consist of different legal entities and a default of the former may be contagious and lead to the default of all others,...