The default rate at the 99.9th percentile (DR₉₉.₉) for Kimpala Leasing Bank is calculated using the formula:

$$\text{DR}_{99.9} = N\left(\frac{N^{-1}(\text{PD}) + \sqrt{\rho} \cdot N^{-1}(0.999)}{\sqrt{1 - \rho}}\right)$$

Given:

• Probability of default (PD): 1% or 0.01
• Correlation parameter (ρ): 0.1216

Using a standard normal distribution table or a calculator, we find:

• $N^{-1}(0.01) \approx -2.33$
• $N^{-1}(0.999) \approx 3.09$

Plugging these values into the formula, we get:

$$\text{DR}_{99.9} = N\left(\frac{-2.33 + \sqrt{0.1216} \cdot 3.09}{\sqrt{1 - 0.1216}}\right) = N(-1.3364)$$

Using the standard normal cumulative distribution function, we find:

$$\text{DR}_{99.9} \approx N(-1.3364) \approx 1 - 0.9093 = 0.0907$$

Therefore, the default rate at the 99.9th percentile for Kimpala Leasing Bank is approximately 9.07%.