Probability of Default Uncertainty in the Vasicek Credit Risk Framework

Abstract

After the recent financial crisis (2007-2010), many doubts on the reliability of the mathematical models to measure the financial risks have arisen. As a consequence, model risk has been a source of concern for financial regulators. This risk includes, among others, incorrect mathematical modelling, inaccurate model inputs calibration or inappropriate model application. In this paper we explore the possible effects of the uncertainty in the calibrated probability of default (PD) on the Basel capital requirements. We also propose two approximated formulas to account for the effect of this uncertainty on, respectively, single and multiple correlated portfolios. Using S&P data and a portfolio of European sovereign bonds, our main empirical conclusion is that the PD uncertainty has not a relevant impact on the risk measurement.