FRM questions by bionic turtle

Question #1 [source 2006 #62]
Many financial applications are concerned only with extreme values of returns or exceptional losses for which we use extreme value distributions (EVD). The following is/are example(s) of EVDs:

I. Weilbull distribution
II. Frechet distribution
III. Generalized Pareto distribution
IV. Student’s t distribution

a. I and II
b. I, II and III
c. IV only
d. II and III

Question #2 [source: me, Dowd Chapter 7]:
Generalized extreme value (GEV) theory provides a natural way to model the maxima or minima of a large sample (block maxima). However, the peaks-over-threshold (POT) approach provides a natural way to model exceedances over a high threshold. Which of the following are true in comparing/contrasting GEV versus POT:

I. They are essentially equivalent
II. GEV can involve a loss of data
III. GEV has fewer parameters
IV. Downside of POT is that it requires selecting a threshold

a. I and III
b. II and IV
c. IV only
d. II, III and IV

Answer #1: B
Weilbull and Frechet distributions are examples of Generalized Extreme Value distributions. Both distributions are used to model maximal loss. Generalized Pareto distribution is used to model excess over a threshold. However, Student’s t distribution is not an example of EVD and cannot be used for modeling extreme values.

Answer #2: B.
I is false; both are EVT, but they are not the same.
II is true: “the most popular GEV approach, the block maxima approach (which we have implicitly assumed so far), can involve some loss of useful data relative to the POT approach, because some blocks might have more than one extreme in them”
III is false as GEV has three params and POT has two params: “TheGEV typically involves an additional parameter relative to the POT”
IV is true: “the POT approach requires us to grapple with the problem of choosing