5 research outputs found
Modelling Correlations in Portfolio Credit Risk
The risk of a credit portfolio depends crucially on correlations between the
probability of default (PD) in different economic sectors. Often, PD
correlations have to be estimated from relatively short time series of default
rates, and the resulting estimation error hinders the detection of a signal. We
present statistical evidence that PD correlations are well described by a
(one-)factorial model. We suggest a method of parameter estimation which avoids
in a controlled way the underestimation of correlation risk. Empirical evidence
is presented that, in the framework of the CreditRisk+ model with integrated
correlations, this method leads to an increased reliability of the economic
capital estimate.Comment: 5 pages, 4 figure
A rule of thumb for the economic capital of a large credit portfolio
We derive approximate formulae for the credit value-at-risk and the economic capital of a large credit portfolio. The representation allows to change the risk horizon quickly and avoids simulation or numerical procedures. The Poisson mixture model is equivalent to CreditRisk+ and uses the same parameters
Truncating the exponential with a uniform distribution
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution. Hence, the data is a truncated empirical process that we can approximate by a Poisson process when only a small portion of the sample is observed, as is the case for our applications. We derive the likelihood from standard arguments for point processes, acknowledging the size of the latent sample as the second parameter, and derive the maximum likelihood estimator for both. Consistency and asymptotic normality of the estimator for the Exponential parameter are derived from standard results on M-estimation. We compare the design with a simple random sample assumption for the observed durations. Theoretically, the derivative of the log-likelihood is less steep in the truncation-design for small parameter values, indicating a larger computational effort for root finding and a larger standard error. In applications from the social and economic sciences and in simulations, we indeed, find a moderately increased standard error when acknowledging truncation