Apr 09

Extreme Value Theory: Intro - 8.5 minute screencast

by David Harper, CFA, FRM, CIPM

Extreme value theory (EVT) aims to remedy a deficiency with value at risk (i.e., it gives no information about losses that breach the VaR) and glaring weakness of delta normal value at risk (VaR): the dreaded-fat tails. Before grappling with the EVT distributions (GPD & GED), I think it's helpful to dwell on the cumulative distribution function (CDF) given by Wilmott (for FRM candidates) under peaks over threshold (POTS). This cumulative distribution is the essence of EVT: P[ x-u < y | x > u].

Note about this probability distribution:

It's a cumulative CDF (versus a PDF or PMF)
It's the probability of a conditional loss: what is the probability that an excess loss (X minus the threshold) will be less than or equal to some value (y) conditional on the loss (X) exceeding the threshold.
The whole thing is a "child distribution" within the "parent distribution" that characterizes central tendency.
For example, if we refer to the 90% EVT, we are not referring to 90% within the parent distribution, but 90% "to the right" within the child EVT. The child distribution starts at the threshold (u), which is the 0% EVT. The 0% EVT might be, just to illustrate, the 95% or 99% "parent" VaR

Here is the screencast: