EVTと呼ばれるリスク管理の計算方法

まだある確立でそんする金額「VAR]にかんする論文を読んでいます。
The section of the paper I have read most recently discusses Extreme Value Theory, or EVT. This seems to be an alternative to GARCH and the historical method for estimating the quantile (amount for which the probability of losing as much or more is theta percent). The first term mentioned is the extreme value distribution, or EVD. This is based on the maximum of some sequence of n random variables {X1,X2,...Xn}, called Mn. It seems H is a function of cn^(-1)(Mn-dn), where cn and dn are constants. It seems that this is the probability that the return is equal to or worse than the max is given by this, although I have yet to confirm this.
Fisher and Tippett demonstrated that H above is:
H(xi)(x)=e^(-(1+xi*x)^(-1/xi)) where 1+xi*x>0
I am not sure what the numerical results of trial inputs to this formula would look like.
The next definition introduced is Maximum Domain of Attraction, or MDA. A variable (or distribution thereof) is an element of MDA(H) if Fisher-Tippett holds for X with limit distribution H. I am not sure what exactly a limit distribution is, but assume it refers to the definition of H above.
The next transition is from excess distributions to Generalized Pareto Distributions (GPD).
The excess distribution is P(Xi-u<=y|Xi>u) for y>=0 and threshold u. It is also written as Fu(y).
In the case where the distribution F element of MDA(H), Fu(y)=G(xi,beta)(y), where G(xi,beta) is the GPD.　Estimates are computed for xi and beta via maximum likelihood, which I do not understand.
Finally, define F(u+y) as the probability that the return is equal to or worse than u+y, with u being the lower bound and y being the excess. 1-F(u+y) = (1-F(u))(1-Fu(y)), as this is the probability that return is greater/equal u times probability that return is not less than or equal to y more than u, given it is greater than u. In other words, the probability that the return is better than u+y. This can be approximated as (N/n)(1-G(xi,beta)(y)). Substituting for G(xi,beta)(y) as:
1-(1+xi*y/beta)^(-1/xi) for appropriate B, y, and xi ranges, we can solve for u+y by solving an equation with 1-(1-F(u+y)) to obtain the value of a return in the quantile desired (i.e. return such that the probability of equal or worse return is the desired probability).
u+y = u+((1-p)(n/N)^(-xi)-i)(beta/xi)
N is the number of Xi greater than u, p is F(u+y). n is number of Xi.
I am uncertain about the accuracy of this model as compared with other VaR models, but the authors conduct Monte Carlo simulation later in the paper to test it.