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3、Empirical research suggests that most severity distributions for operational risk are extremely “heavy” tailed. To be compliant with Basel II, the extreme heavy-tailed property of operational losses needs to be accounted for in the choice of the severity distribution. Which of the following statements are TRUE with respect to severity distributions?

Three well-known heavy-tailed distributions are the Poisson, Weibull, and the Pareto distribution.
Of the Poisson, Weibull, and Pareto distribution only the Pareto is consider subexponential.
Subexponential distributions are distinct statistically in that their tails decay more slowly than any exponential distribution.
Heavy-tailed distributions have large, but well-defined means and variances.
A) II only.
 
B) I only.
 
C) All of these.
 
D) III only.
 

nayizhenfeng

The correct answer is D

Poisson is not considered a “heavy” tailed distribution. The Poisson, Weibull, and Pareto distributions are all in the subexponential class. The natural logarithm of 1 is 0, since e0 = 1.

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AIM 3: Discuss the implications the closed-form operational VAR has on the general class of LDA models.

 

1、Operational losses are best approximated with:

A) exponential distributions.
 
B) skewed distributions.
 
C) heavy tailed distributions.
 
D) bimodal distributions.

nayizhenfeng

The correct answer is C

Operational losses are best captured with heavy-tailed distributions as these losses tend to be sizable.

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2、Past Research has shown, very conclusively, that when it comes to modeling operational risk:

heavy tailed distributions are not needed.
extreme events occur frequently enough that the mean is often undefined.
standard deviation is remarkably consistent.
standard deviations are likely undefined.
A) II and IV only.
 
B) II and III only.
 
C) I and II only.
 
D) III only.

nayizhenfeng

The correct answer is A

Heavy tailed distributions are needed. Standard deviation is often undefined.

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AIM 4: Explain the time-scaling in the Pareto Severity Model and its implications.

 

1、In the case of the Pareto-LDA model, typical values for α imply that the threat of losses due to operational risk increases very quickly, notably faster than the result of the square-root-rule. This result suggests:

A) operational risk rapidly decreases with time.
 
B) operational risk is greatest at time, t = 0.
 
C) operational risk increases with time.
 
D) operational risk is independent of time.

nayizhenfeng

The correct answer is C

As time increases operational risk increases.

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2、In practice one can derive multi-period VAR measures from 1-period values by:

A) using the LDH approach.
 
B) using the square root of time rule.
 
C) multiplying the VAR measures.
 
D) adding the VAR measures.

nayizhenfeng

The correct answer is B

In practice multiperiod VaR measures can be derived by using the square-root of time rule.