Abstract
The CreditRisk+ model is one of the industry standards for the valuation of default risk in credit loans portfolios. The calibration of CreditRisk+ requires, inter alia, the specification of the parameters describing the structure of dependence among default events. This work addresses the calibration of these parameters. In particular, we study the dependence of the calibration procedure on the sampling period of the default rate time series, that might be different from the time horizon onto which the model is used for forecasting, as it is often the case in real life applications. The case of autocorrelated time series and the role of the statistical error as a function of the time series period are also discussed. The findings of the proposed calibration technique are illustrated with the support of an application to real data.
Highlights
IntroductionWhile the development of modern portfolio credit risk models started in the 1980–1990 decade [1] within the framework of the Basel Accords, it is with the great credit crisis of
While the development of modern portfolio credit risk models started in the 1980–1990 decade [1] within the framework of the Basel Accords, it is with the great credit crisis of2008 [2] that increasing attention started to be paid to the precise determination of the structure of dependence among default events
We study the dependence of the calibration procedure on the sampling period of the default rate time series, that might be different from the time horizon onto which the model is used for forecasting, as it is often the case in real life applications
Summary
While the development of modern portfolio credit risk models started in the 1980–1990 decade [1] within the framework of the Basel Accords, it is with the great credit crisis of. We address a typical real-life problem: how to choose the frequency of the historical time series of default used to calibrate a classic credit portfolio model, CreditRisk+ , in order to provide the most accurate estimation of the structure of dependence parameters, or, in other words, how the calibration error “scales” with the time series frequency. Equation (12) allows the calibration of the factor loadings, and of the dependence structure of the CreditRisk+ model, by matching the observed covariance matrix of historical default time series with model values. Since the model is defined in a single-period framework, with a reference “forecasting” time horizon (t, T ], that is typically of 1 year, i.e., T = t + 1, it is not a priori evident how to use historical time series with a different frequency (e.g., quarterly) in a consistent way, when calibrating the model parameters.
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