We first determine the 99.9% worst-case default rate, $V(X, T)$:

$$v(x, \rho) = N\left(\frac{N^{-1}(P(T)) + \sqrt{\rho} N^{-1}(X)}{\sqrt{1 - \rho}}\right)$$

Therefore,

$$V(0.999, 0.20) = N\left(\frac{N^{-1}(0.025) + \sqrt{0.20} N^{-1}(0.999)}{\sqrt{1 - 0.20}}\right) = N\left(\frac{-1.9599 + \sqrt{0.20} \times 3.0902}{\sqrt{0.80}}\right) = N(-0.6461) = 0.2591$$

Therefore, the 1-year Credit VaR at the 99.9% (note: text says 99.5% in the final line, but calculates for 99.9%) confidence level is:

\`$300`\text{ million} \times 0.2591 \times (1 - 0.40) = \`$46.64`\text{ million}

Things to Remember

• Credit Value at Risk (Credit VaR) is a statistical technique used to measure and quantify the level of financial risk within a portfolio.
• The probability of default (PD) is a key component in credit risk modeling, representing the likelihood that a borrower will be unable to meet its debt obligations.
• Recovery rate is the percentage of principal and interest that is recovered by the lender in the event of a default.