3.md 2.5KB
2.1.Highlights of the IRB setup and evolution
individual borrower’s level.
More than a decade later, the concept to consider a bunch of such individual borrowers was developed in Vasicek (1987). The starting point was to decompose the individual borrowers’ pattern into specific (idiosyncratic) and common (systemic) components as in Eq. (1).
$$ A{i}=Z\cdot r+u{i}\cdot\sqrt{1-R} $$
where - common factor; $u_{i}\sim N(0,1)$ -specific factor$ ,$
$r=\mathrm{corr}(A_i,Z)$ $$ \rho \text{ (conventional mathematical correlation) as it originally appeared without a squared power in the works by Vasicek (1987); Gordy (2000)} \text{ (let us call it default correlation):} $$
(R=r^{2}) - asset (value) correlation using BCBS notations (mathematically speaking, it is the square of the conventional mathematical correlation between (A_{i}) and (Z)).
Due to the nice properties of the Gaussian distribution, Vasicek uses the Value-at-Risk (VaR) measure to slice the default rate (DR) distribution of the loan portfolio and arrives at the most feasible default rate realization given the chosen significance level of α in Eq. (2).
$$ V a R=N\left(\frac{N^{-1}(PD)+N^{-1}(1-\alpha)\cdot\sqrt{R}}{\sqrt{1-R}}\right). $$
Important to note that Vasicek did not impose any restrictions on ( r ) over its feasible values. The only thing he notes is that in case ( r > 50\% ), the DR distribution becomes U-shaped (bimodal). Remembering the notations that ( R = r^2 ) or ( r = \sqrt{R} ), we should take away that Vasicek was speaking of DR distribution bimodality when the asset (value) correlation exceeds 25% (( R > 25\% )).
006 BCBS amendment to the Vasicek model. The idea to internationally introduce model-based (IRB) credit risk regulation seems to have become popular after the success of such regulation introduction for the market risk in the Basel I amendment BCBS (1996). Thus, the very first draft of the future Basel II Accord incorporating IRB appeared on the edge of the new millennium, see Penikas (2020a), while it
When designing IRB, the Basel Committee implemented five conceptual amendments, originally not previewed in the Vasicek model:
BCBS chose the IRB significance level of $\alpha=0.1\%$ (inversely, confidence level of 99.9\%) which corresponds to the risk-measure breach (bank failure) once in one hundred years given the annual horizon for PD, see BCBS (2005a).
BCBS added other credit risk parameters like loss given default (LGD), exposure at default (EAD), maturity (M) etc. For instance, VaR from Eq. (2) is multiplied by LGD and EAD.