Journal of Risk

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Parameter estimation, bias correction and uncertainty quantification in the Vasicek credit portfolio model

Marius Pfeuffer, Maximilian Nagl, Matthias Fischer and Daniel Rösch

  • We approximate standard errors for Value-at-Risk and Expected Shortfall based on standard errors of intra-cohort correlations. These can be used to quantify a margin of conservatism required by regulators.
  • A novel copula based approach to estimate inter-cohort correlations is introduced, which outperforms current estimators.
  • We show that resampling methods reduce the bias of current estimators substantially.
  • We introduce the R Package AssetCorr, which includes a majority of current available estimators, bias correction procedures and uncertainty quantification methods.

This paper is devoted to the parameterization of correlations in the Vasicek credit portfolio model. First, we analytically approximate standard errors for value-at-risk and expected shortfall based on the standard errors of intra-cohort correlations. Second, we introduce a novel copula-based maximum likelihood estimator for inter-cohort correlations and derive an analytical expression of the standard errors. Our new approach enhances current methods in terms of both computing time and, most importantly, direct uncertainty quantification. Both contributions can be used to quantify a margin of conservatism, which is required by regulators. Third, we illustrate powerful procedures that reduce the well-known bias of current estimators, showing their favorable properties. Further, an open-source implementation of all estimators in the novel R package AssetCorr is provided and selected estimators are applied to Moody’s Default & Recovery Database.

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