Answer: The model coefficient $a$ directly relates to the correlations between the default probability distributions $U_i$ of the loans in the portfolio.

## Explanation **D is correct.** The correlation between each pair of $U_i$ distributions is equal to $a^2$. **Why other options are incorrect:** - **A is incorrect:** The default probabilities are each mapped to the standard normally distributed variable $U_i$, however, values in the extreme left tail represent default. As such, low values of $F$ or $Z_i$ correspond with a higher likelihood of default. - **B is incorrect:** High values of $F$ indicate a strong economy, and low values of $F$ indicate a weak economy. As such, low values of $F$ correspond with a higher likelihood of default. - **C is incorrect:** $F$ is a common factor and is equal for all loans in the portfolio. It does not vary based on the cyclical nature of individual companies' businesses. ## Key Concepts The Vasicek model uses the equation: $$U_i = aF + \sqrt{1 - a^2} Z_i$$ Where: - $U_i$ represents the asset value of firm i - $F$ is the common systematic factor - $Z_i$ is the idiosyncratic factor - $a$ is the factor loading that determines the correlation between firms The correlation between any two firms' asset values is $a^2$, making the coefficient $a$ directly related to the default correlations in the portfolio.

Author: LeetQuiz .