Explanation:
The correct answer is C.
The default probability correlation distribution can be best modeled using the Johnson SB distribution, whereas the correlation distribution can be best modeled using the generalized extreme value distribution. The default probability correlation distribution is akin to the equity correlation distribution and can be best replicated using the Johnson SB distribution. This distribution is flexible and can model a wide range of shapes, making it suitable for modeling the default probability correlation distribution. On the other hand, the bond correlation distribution exhibits a more normal shape and can be best modeled using the generalized extreme value distribution. This distribution is used for modeling extreme values and is suitable for modeling the bond correlation distribution which tends to have extreme values. It's important to note that the bond correlation distribution can also be quite well replicated using the normal distribution, which is a testament to its normal shape.
Choice A is incorrect. While the Johnson SB distribution can model a wide range of shapes and may be used in some cases, it is not the best fit for both default probability correlation distribution and bond correlation distribution. The two distributions have different characteristics and hence require different modeling approaches.
Choice B is incorrect. The assertion that the default probability correlation distribution shows a normal shape is inaccurate. In reality, this distribution often exhibits skewness or kurtosis, which are not characteristics of a normal shape. Therefore, using the generalized extreme value distribution to model it would not be appropriate.
Choice D is incorrect. As explained above, both distributions have distinct characteristics and thus cannot be accurately modeled using the same statistical distribution — in this case, the generalized extreme value distribution.
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Q.1566 Bonds and their default probabilities also have correlation distributions just like equity. Which of the following best describes the default probability correlation distribution and correlation distribution for bonds?
A
Both the default probability correlation distribution and the correlation distribution can be best modeled using the Johnson SB distribution.
B
The default probability correlation distribution shows a normal shape and can be best modeled using the generalized extreme value distribution, whereas the correlation distribution can be best modeled using the Johnson SB distribution.
C
The default probability correlation distribution can be best modeled using the Johnson SB distribution, whereas the correlation distribution can be best modeled using the generalized extreme value distribution.
D
Both the default probability correlation distribution and the correlation distribution can be best modeled using the generalized extreme value distribution.