the question of Value at risk in Tsay (2005) p.313

[Frank]

Hi, Tom

I use WinRats 6.35. As I refer the sample codes in the textbook of Tasy's Analysis of F.T. series.
in the sample code of p.313, it is calculating value at risk (VaR) based on extreme value theory. And it uses
the code as :

compute var01=%invgev((1-.01)**n,k,-beta,alpha)

From Tasy's book p.312-313, it seems calculating VaR with eq. (7.28), right ?
but, the code used " %invgev((1-.01)**n,k,-beta,alpha) " to computed VaR, it is eq. (7.26), right?

since " %invgev() " is just inverse the distribution of GEV, is it calculating VaR on original return level ?

however, it's interesting that as I can't obtain the number "-3.04939" but can get "-12.9342", calculating VaR based on eq. (7.26).
the question:
no.1, is " %invgev()" just only inverse the GEV distribution in extreme level or original return level ?
no.2, is this sample code calculating Var based on eq.(7.26) or (7.28) ?

thanks


Frank

[TomDoan]

In Tsay, (7.26) and (7.28) are the same formulas---it's just that (7.28) is using a specific value for p*. Part I is showing how to invert the GEV, while Part II figures out what probability needs to be input to the GEV inverse to get the desired value. (7.28) is what's being calculated for a VaR.

[Frank]

In Tsay, (7.26) and (7.28) are the same formulas---it's just that (7.28) is using a specific value for p*. Part I is showing how to invert the GEV, while Part II figures out what probability needs to be input to the GEV inverse to get the desired value. (7.28) is what's being calculated for a VaR.

Hi Tom

I agree your saying. but in the sample code to this example, it seems using (7.26) to calculate VaR, but it has another part, the exponent of n. since %invgev is to inverse gev distribution which is based on (7.26), does it mean that (7.26) will become (7.28)
after adding the exponent ?


Frank

[TomDoan]

The GEV is the result of an odd form of asymptotic distribution since the actual maximum value --> infinity asymptotically for any underlying distribution with unbounded support. For the VaR, we don't want the maximum value, but instead want a tail probability. However, if the sample is (approximately) independent, then P(max <= x) = P(X<=x)^n. You use the extreme value distribution to solve the left side for x, given a chosen value for P(X<=x). The page plus of algebra in Tsay is showing how to do that.