Learning outcomes: Define copula, describe the key properties of copula and copula correlation. Explain one tail dependence. Describe Gaussian copula, Student t-copula, multivariate copula and one factor copula.
Questions:
504.1. In regard to copulas, each of the following is true EXCEPT which is false?
a. A copula is a way of defining the correlation between variables with known distributions.
b. Copulas cannot be used to define a correlation structure between more than two variables
c. The one-factor Gaussian copula model leads to very little tail dependence, which is a limitation of the model
d. The Gaussian copula is just one copula that can be used to define a correlation structure between marginal distributions; there are many other copulas leading to many other correlation structures.
504.2. Consider the following three statements about tail dependence:
I. Tail dependence is the tendency for extreme values for two or more variables to occur together
II. The choice of the copula affects tail dependence
III. The tail dependence is higher in a bivariate Student t-distribution than in a bivariate normal distribution.
Which of the above is (are) true?
a. None are true
b. Only I. is true
c. Only III. is true
d. All are true
504.3. Suppose that a bank has a total of $100.0 million of retail exposures of varying sizes with each exposure being small in relation to the total exposure. The one-year probability of default (PD) for each loan is 3.0% and the loss given default (LGD) for each loan is 60.0%. The copula correlation parameter, rho(ρ), is estimated as 0.250. Which is nearest to an estimate of the value at risk with a one-year time horizon and a 99.9% confidence level? (note: this is a variation on Hull's example 11.2)
a. $8.41 million
b. $12.57 million
c. $20.95 million
d. $36.72 million
Answers here:
Questions:
504.1. In regard to copulas, each of the following is true EXCEPT which is false?
a. A copula is a way of defining the correlation between variables with known distributions.
b. Copulas cannot be used to define a correlation structure between more than two variables
c. The one-factor Gaussian copula model leads to very little tail dependence, which is a limitation of the model
d. The Gaussian copula is just one copula that can be used to define a correlation structure between marginal distributions; there are many other copulas leading to many other correlation structures.
504.2. Consider the following three statements about tail dependence:
I. Tail dependence is the tendency for extreme values for two or more variables to occur together
II. The choice of the copula affects tail dependence
III. The tail dependence is higher in a bivariate Student t-distribution than in a bivariate normal distribution.
Which of the above is (are) true?
a. None are true
b. Only I. is true
c. Only III. is true
d. All are true
504.3. Suppose that a bank has a total of $100.0 million of retail exposures of varying sizes with each exposure being small in relation to the total exposure. The one-year probability of default (PD) for each loan is 3.0% and the loss given default (LGD) for each loan is 60.0%. The copula correlation parameter, rho(ρ), is estimated as 0.250. Which is nearest to an estimate of the value at risk with a one-year time horizon and a 99.9% confidence level? (note: this is a variation on Hull's example 11.2)
a. $8.41 million
b. $12.57 million
c. $20.95 million
d. $36.72 million
Answers here:
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