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2、Extreme value theory can assist with VAR calculations by providing better probability estimates of extreme losses than those indicated by a standard normal distribution. Using the generalized Pareto distribution (GPD), the parameter that indicates the fatness of tails is the:

A) threshold level, μ.

B) scaling parameter, b.

C) slope coefficient, b.

D) shape parameter, ξ.

aianjie

 

The correct answer is D

A positive shape parameter, ξ, indicates fat tails.

aianjie

 

3、The generalized extreme value (GEV) distribution is useful for: I. estimating VAR. II. stress testing. III. estimating correlation. IV. backtesting.

A) I, II, III, and IV.

B) I and III only. 

C) I only. 

D) II only. 

aianjie

 

The correct answer is D

The GEV distribution describes the distribution of the maximums from a large sample of identically distributed observations. It’s not particularly useful for VAR estimation since VAR does not consider the distribution of the maximum, but it is useful for stress testing. GEV also has nothing to do with correlations and would not be used for backtesting to see if a VAR model was effective.

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4、Extreme value theory (EVT) can assist with value at risk (VAR) calculations by providing better probability estimates of observing extreme losses than that indicated by a standard normal distribution because empirical distributions exhibit fat tails. If one uses the generalized Pareto distribution (GPD) method to generate parameter estimates for the shape parameter, fat tails will indicate a:

A) positive parameter estimate and VAR calculations that are too small.

B) positive parameter estimate and VAR calculations that are too large.

C) negative parameter estimate and VAR calculations that are too small.

D) negative parameter estimate and VAR calculations that are too large.

aianjie

 

The correct answer is A

Fat tails will generate a positive shape parameter, which indicates that VAR estimates are probably too small.

aianjie

 

5、Block maxima disaggregates the data into:

A) equal sized, independent subsamples. 

B) unequal sized, independent subsamples. 

C) unequal sized, dependent subsamples. 

D) equal sized, dependent subsamples. 

aianjie

 

The correct answer is A

The block maxima approach determines the maxima for mutually exclusive, equal sized, independently distributed subsamples of data.

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6、Which of the following statements is TRUE?

A) The semi-parametric peaks-over-threshold utilizes the generalized Pareto distribution. 

B) Block maxima are a semi-parametric peaks-over-threshold model. 

C) Tail events are more likely under the generalized Pareto distribution relative to a normal distribution. 

D) The generalized Pareto distribution provides a non-linear estimate of the tail. 

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The correct answer is C

Generalized Pareto distribution generates a linear approximation to the tail distribution. Block maxima and peaks-over-threshold are two general classes of extreme value modeling. The generalized Pareto distribution is a parametric approach.