The three follow-up articles will discuss how extreme value theory has been applied to VaR and compare it to the more traditional VaR approaches. A major problem facing VaR practitioners is that the VaR is an extreme quantile on a return distribution, and yet we have relatively few extreme observations with which to estimate it. Our VaR estimates are therefore imprecise, and become even more so as we move further out into the tail of the distribution.
Practitioners have to respond by relying on assumptions to make up for lack of data.
However, the assumptions they make are often questionable. A common assumption is that portfolio returns are normally distributed. A more satisfactory assumption is that returns follow a fat-tailed distribution. A suitable distribution is then chosen and estimated using all the data. However, since most observations are central ones, the distribution is constructed to fit the central observations best, and is therefore ill suited to the extreme observations with which we are mainly concerned.