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Answer: The model coefficient a directly relates to the correlations between the default probability distributions Ui of the loans in the portfolio.
The correct answer is D. The model coefficient 'a' directly relates to the correlations between the default probability distributions U_i of the loans in the portfolio. The Vasicek model is a credit risk model that estimates the probability of default for a portfolio of loans. In this model, the default rate is a function of a common factor F and individual loan characteristics represented by z_i. The correlation between each pair of U_i distributions, which represent the default probabilities of individual loans, is determined by the coefficient 'a' squared (a^2). This means that 'a' plays a crucial role in capturing the systemic risk or the common movements in the economy that affect the default probabilities of all loans in the portfolio. The other options are incorrect for the following reasons: A is incorrect because the default probabilities are mapped to the standard normally distributed variable U_i, with values in the extreme left tail representing default, not the right tail. B is incorrect as a high value of F indicates a strong economy, which would correspond to a lower likelihood of default, not a high value indicating economic weakness. C is incorrect because F is a common factor affecting all loans in the portfolio equally, rather than being higher for loans to companies with more cyclical businesses.
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Ui = aF + √(1-α²)zi
N⁻¹(PD) = aF
The default rate, expressed in terms of F, is provided by N(√(1-α²)).
A
The default probabilities of the individual loans in a portfolio are each mapped to the standard normal distribution Ui, of which values in the extreme right tail represent default.
B
A low value of the factor F indicates that the economy is strong, while a high value of F represents economic weakness.
C
For corporate borrowers, the value of the factor F is higher for loans to companies with more cyclical businesses.
D
The model coefficient a directly relates to the correlations between the default probability distributions Ui of the loans in the portfolio.
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