Under the Basel II Internal Ratings-Based (IRB) approach, the regulatory capital requirement is meant to cover Unexpected Loss (UL) and is calculated using the Vasicek single-factor model:

Step 1: Calculate the Worst-Case Default Rate (WCDR) The formula for WCDR at the 99.9% confidence level is: $WCDR = N \left( \frac{N^{-1}(PD) + \sqrt{R} \times N^{-1}(0.999)}{\sqrt{1 - R}} \right)$ Given:

• $PD = 0.02 \Rightarrow N^{-1}(0.02) \approx -2.0537$
• $R = 0.25 \Rightarrow \sqrt{R} = 0.5 \text{ and } \sqrt{1 - R} = \sqrt{0.75} \approx 0.8660$
• $N^{-1}(0.999) \approx 3.0902$

$WCDR = N \left( \frac{-2.0537 + (0.5 \times 3.0902)}{0.8660} \right)$ $WCDR = N \left( \frac{-2.0537 + 1.5451}{0.8660} \right) = N \left( \frac{-0.5086}{0.8660} \right) = N(-0.5873)$ Using the standard normal cumulative distribution, $N(-0.5873) \approx 0.2785$ (or 27.85%).

Step 2: Calculate the Unexpected Loss (UL) Regulatory capital is required for Unexpected Loss, as Expected Loss is covered by provisions: $UL = EAD \times LGD \times (WCDR - PD)$ Given:

• EAD = \`120` \text{ million}$
• $LGD = 1 - \text{Recovery Rate} = 1 - 0.40 = 0.60$

$UL = 120 \times 0.60 \times (0.2785 - 0.02)$ UL = 72 \times 0.2585 = \`$18.61` \text{ million}

The regulatory capital requirement is `$18.61` million.