A1508
Title: Parameter estimation and bias correction in the Vasicek credit portfolio model
Authors: Marius Pfeuffer - University of Erlangen-Nuremberg (Germany) [presenting]
Abstract: Credit portfolio modeling is an important aspect of quantitative risk management and the Vasicek model with asset variables $A_{ij}=\sqrt{\rho_i}\Psi_i+\sqrt{1-\rho_i}\epsilon_j$, where $\boldsymbol{\Psi}\sim\mathcal{N}(\mathbf{0},\{\rho_{i_1,i_2}\}_{1\leq i_1,i_2\leq I})$ is a systematic and $\epsilon\sim\mathcal{N}(0,1)$ an idiosyncratic component is a core approach to describe dependencies for a set of obligors $1,\ldots,J$ in cohorts (e.g., rating categories) $1,\ldots,I$. In order to parameterize this model, moment or maximum likelihood estimators for the correlation parameters are usually employed. First, a systematic overview of the existing estimation approaches in the literature is given. Second, as empirical studies report that asset correlation estimates are often biased, this effect is analyzed and possible methods for bias reduction are discussed. It is especially shown that what in the literature is considered as moment estimators is based on the asymptotic behavior of the Binomial-Vasicek compound distribution. The moment estimators for the complete model are derived and its behavior is illustrated. Moreover, resampling approaches for bias reduction are employed. Third, theoretical properties of inter-asset Pearson correlations $\rho_{i_1,i_2}$ between different cohorts are outlined and benchmarked against other measures of dependence. The methods are illustrated by hypothetical simulation studies and Standard and Poor's ratings data.
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