The Worst-Case Default Rate (WCDR) at the 99.9% confidence level is calculated using the Vasicek model formula: $WCDR = N\left( \frac{N^{-1}(PD) + \sqrt{\rho} N^{-1}(0.999)}{\sqrt{1 - \rho}} \right)$

Given the variables:

• $PD = 2.0\% \Rightarrow N^{-1}(0.02) = -2.0537$
• $\rho = 0.130 \Rightarrow \sqrt{\rho} = \sqrt{0.13} = 0.3606$
• Confidence level $= 99.9\% \Rightarrow N^{-1}(0.999) = 3.0902$

Substitute the values: $WCDR = N\left( \frac{-2.0537 + (0.3606 \times 3.0902)}{\sqrt{1 - 0.13}} \right)$ $WCDR = N\left( \frac{-2.0537 + 1.1143}{\sqrt{0.87}} \right)$ $WCDR = N\left( \frac{-0.9394}{0.9327} \right) = N(-1.0072)$

Using the standard normal cumulative distribution, $N(-1.0072) \approx 15.69\%$.

The Unexpected Loss (which matches Credit VaR per Malz definition) is defined as the difference between the Worst-Case Loss and the Expected Loss: $UL = (WCDR - PD) \times LGD \times EAD$

Given that Recovery Rate is 50.0%, $LGD = 1 - 0.50 = 50.0\%$. UL = (15.69\% - 2.00\%) \times 50.0\% \times \`$100.0` \text{ million} UL = 13.69\% \times \`$50.0` \text{ million} = \`$6.84`5 \text{ million}