Weibull vs. Frechet

[ahnnecabiles]

Hi David,

In the EVT distribution of market risk, fat tails are referred to as the "frechet" (shape of the distribution). However, in the LDA distribution, fat tails are referred to as the "Weibull" (which has "thin tails" shape from our quanti readings). Both are referring to extreme losses, but why are they using different shape parameter?

Thanks.

 

[David Harper CFA FRM]

Chinquee,

That's observant, this is a deep subject. They both (Weibull and Frechet) can refer to fat/heavy tails, technically. The problem arises because the EVT reading is typically imprecise in describing GEV. It's not a Weibull but rather a (reverse) Weibull bounded by a maximum; i.e., so a "reverse Weibull" has "thin tails" and isn't so good for fat-tailed financial returns but a Weibull actually might be okay if unusual. So, bottom line: Wilmott's EVT Weibull is different than the Operational VaR Weibull. In both cases, EVT and OpRisk VaR, it is a quest for a distribution with heavy tails.

Further sometimes the index/shape is used interchangeably; a bit more here.

Here is the bottom line for (practical) exam purposes: the subexponential distributions in OpVaR are so considered due to their fat tails; in EVT GEV, only the Frechet is relevant where higher shape param associates with fatter tails.

David