Suzanne Evans
Well-Known Member
Questions:
213.1. You colleague John wants to employ an extreme value theory (EVT) distribution, either generalized Pareto distribution (GPD) or generalized extreme-value (GEV) distribution, to model the risk of an exposure. He makes the following four arguments, each of which is true, EXCEPT for which one is false?
a. Both EVT distributions are compatible with (can be used as in input into) a value at risk (VaR) metric
b. Both EVT distributions easily model heavy-tails
c. Neither EVT requires specific knowledge of the underlying loss distribution
d. As both EVT distributions are non-parametric, "model risk and estimation risk are effectively eliminated"
213.2. Your assignment is to configure a model for financial market (price-based) losses at your bank. For the extreme tail, you want to fit an EVT distribution, either GPD or GEV, to your internal historical loss dataset. However, your bank's loss data exhibits a high degree of clustering; i.e., time dependency which violates an assumption that the losses are independent and identically distributed (i.i.d.). Which is the best approach, POT or GEV?
a. The clustering is not relevant and you can use either POT or GEV: unlike CLT, neither EVT distribution requires an assumption that the underlying losses are i.i.d.
b. Use the POT (GPD) approach: GEV (block maxima) requires i.i.d. but POT does not, and in fact, anticipates clustering
c. Use the GEV (block maxima) approach: with long enough time blocks, the clustering effect should be mitigated
d. Neither GEV nor POT can be used; there is no currently known method for dealing with non-i.i.d. data under EVT
213.3. You propose to compute the expected shortfall (ES) of a position by employing extreme value theory (EVT) to characterize the loss tail with either a GPD (POT approach) or GEV (block maxima approach) distribution. Your colleague Fred objects with the following criticisms:
I. EVT is incompatible with expected shortfall (ES), you need to choose one approach or the other
II. We are "stuck with" GEV or GPD due to small samples. As the sample size increases, the central limit theorem (CLT) justifies a normal distribution for the extreme loss tail. If our sample is sufficiently large, we should assume a normal distribution
III. To fit either distribution (GPD or GEV), we need to specify both a scale (dispersion) and a tail parameter, but there are no known methods for estimating these parameters with historical data
IV. EVT estimates are uncertain and attach with relatively wide confidence intervals due to their (mostly) asymptotic nature and paucity of data
Which of Fred's criticisms is valid?
a. None are valid
b. Only II. and III.
c. Only IV.
d. All are valid.
Answers:
213.1. You colleague John wants to employ an extreme value theory (EVT) distribution, either generalized Pareto distribution (GPD) or generalized extreme-value (GEV) distribution, to model the risk of an exposure. He makes the following four arguments, each of which is true, EXCEPT for which one is false?
a. Both EVT distributions are compatible with (can be used as in input into) a value at risk (VaR) metric
b. Both EVT distributions easily model heavy-tails
c. Neither EVT requires specific knowledge of the underlying loss distribution
d. As both EVT distributions are non-parametric, "model risk and estimation risk are effectively eliminated"
213.2. Your assignment is to configure a model for financial market (price-based) losses at your bank. For the extreme tail, you want to fit an EVT distribution, either GPD or GEV, to your internal historical loss dataset. However, your bank's loss data exhibits a high degree of clustering; i.e., time dependency which violates an assumption that the losses are independent and identically distributed (i.i.d.). Which is the best approach, POT or GEV?
a. The clustering is not relevant and you can use either POT or GEV: unlike CLT, neither EVT distribution requires an assumption that the underlying losses are i.i.d.
b. Use the POT (GPD) approach: GEV (block maxima) requires i.i.d. but POT does not, and in fact, anticipates clustering
c. Use the GEV (block maxima) approach: with long enough time blocks, the clustering effect should be mitigated
d. Neither GEV nor POT can be used; there is no currently known method for dealing with non-i.i.d. data under EVT
213.3. You propose to compute the expected shortfall (ES) of a position by employing extreme value theory (EVT) to characterize the loss tail with either a GPD (POT approach) or GEV (block maxima approach) distribution. Your colleague Fred objects with the following criticisms:
I. EVT is incompatible with expected shortfall (ES), you need to choose one approach or the other
II. We are "stuck with" GEV or GPD due to small samples. As the sample size increases, the central limit theorem (CLT) justifies a normal distribution for the extreme loss tail. If our sample is sufficiently large, we should assume a normal distribution
III. To fit either distribution (GPD or GEV), we need to specify both a scale (dispersion) and a tail parameter, but there are no known methods for estimating these parameters with historical data
IV. EVT estimates are uncertain and attach with relatively wide confidence intervals due to their (mostly) asymptotic nature and paucity of data
Which of Fred's criticisms is valid?
a. None are valid
b. Only II. and III.
c. Only IV.
d. All are valid.
Answers:
