In the One-Factor Gaussian Copula Model, the creditworthiness value $x_i$ for a company is calculated using the formula:

$$x_i = b_i F + \sqrt{1 - b_i^2} y_i$$

Given that $b_i = 0.7$, $F$ is at the 80th percentile, and $y_i$ is at the 60th percentile of the standard normal distribution:

$$x_i = 0.7 \cdot N^{-1}(0.80) + \sqrt{1 - 0.7^2} \cdot N^{-1}(0.60)$$ $$= 0.7 \cdot 0.8416 + \sqrt{1 - 0.49} \cdot 0.2533$$ $$\approx 0.7701$$

Now, to find the threshold value for $x_i$ that would indicate a default, we use the inverse standard normal distribution of the given probability of defaulting by time $T$, which is 10%:

$$\text{Threshold Value for } x_i = N^{-1}(0.10) \approx -1.2816$$

So, the creditworthiness value $x_i$ for the company is approximately 0.7701, and the threshold value for $x_i$ that would indicate a default is approximately -1.2816.

Things to Remember

• The One-Factor Gaussian Copula Model is used to assess a company's creditworthiness by considering both common and specific economic factors, following standard normal distributions.