The Basel II capital requirement for banks under the IRB approach is given by:

$$(\text{WCDR} - \text{PD}) \times \text{LGD} \times \text{EAD}$$

where WCDR is defined as the worst-case default rate, and it is 99.9 percentile of the default rate distribution defined as in the Vasicek model.

Therefore, we need to calculate WCDR, which is the 99.9 percentile of the default rate based on the Vasicek model.

$$\begin{aligned} 99.9 \text{ percentile for default rate } &= N\left( \frac{N^{-1}(\text{PD}) + \sqrt{\rho} N^{-1}(0.999)}{\sqrt{1 - \rho}} \right) \\ &= N\left( \frac{N^{-1}(0.005) + \sqrt{0.75} N^{-1}(0.999)}{\sqrt{1 - 0.75}} \right) \\ &= N\left( \frac{-2.576 + 0.87 \times 3.09}{\sqrt{0.25}} \right) = N(0.2246) = 0.5889 \end{aligned}$$ $$\Rightarrow (\text{WCDR} - \text{PD}) \times \text{LGD} \times \text{EAD} = (0.5889 - 0.005) \times (1 - 0.4) \times 500 = 175.17$$