To find the regulatory capital requirement, we use the Vasicek Single Factor Model formula for the Worst-Case Default Rate (WCDR): $WCDR = N\left( \frac{N^{-1}(PD) + \sqrt{\rho} N^{-1}(0.999)}{\sqrt{1-\rho}} \right)$ Given:

• $PD = 2\% = 0.02 \implies N^{-1}(0.02) \approx -2.0537$
• $\rho = 0.25 \implies \sqrt{\rho} = 0.5$, $\sqrt{1-\rho} = \sqrt{0.75} \approx 0.8660$
• $99.9% \text{ confidence level} \implies N^{-1}(0.999) \approx 3.0902$

$WCDR = N\left( \frac{-2.0537 + 0.5 \times 3.0902}{0.8660} \right) = N\left( \frac{-2.0537 + 1.5451}{0.8660} \right) = N(-0.5873) \approx 27.85\%$

Regulatory capital is designed to cover unexpected losses (UL), calculated as: $\text{Capital Requirement} = EAD \times LGD \times (WCDR - PD)$

• EAD = \`120` \text{ million}$
• $LGD = 1 - \text{Recovery Rate} = 1 - 0.40 = 0.60$ $\text{Capital Requirement} = 120 \times 0.60 \times (0.2785 - 0.02) = 72 \times 0.2585 \approx 18.61 \text{ million}$.