Large deviations theory and extreme value theory

I'll enter into details of both, sooner or later, but for the moment I'm concerned about the differences (and relationships, if any) between these two theories. Can someone give me a brief, but still a little technical, explanation of the divergences (common points) of these theories? Thank you all.

• Extreme Value theory is concerned with the prob. dist. of the maximum (or minimum) of several random variables. For example the rainfall in centimeters is measured every day at a certain location; what can we say about the maximum yearly rainfall (that is the max of the 365 daily values for one calendar year)? Large deviations theory, I am less familiar with, is concerned with the behavior of their tails of the distribution of a r.v. as a parameter N becomes large. The Central Limit theorem tells you what happens to the mean, the LD Theory tells you about the tails. – noob2 Jan 11 '16 at 18:51
• Thank you. Well, suppose you want to the estimate the Value at Risk of one stock (as a starting point; I know that they are used to this purpose, too): how do they differ in the estimation? Why and when is better one or the other? – simmy Jan 11 '16 at 20:17
• I considered the application of EVT to the calculation of VaR a few years ago. But I concluded from a paper by Diebold that EVT is not really necessary for the calculation of 5% or 1% VaR as these are not extreme enough; it might help in estimating the 0.1% events if you are interested in those. Also EVT assumes that variables are iid, which is not the case for stock returns due to GARCH effects. ssc.upenn.edu/~fdiebold/papers/paper21/dss-f.pdf So I have never used EVT methods for VaR. – noob2 Jan 11 '16 at 21:25
• @noob2 It seems interesting. However, in this paper of McNeil & Frey (2000) link a conditional approach to the EVT is (succesfully, it seems) applied to the VaR and CVaR estimation. What do you think about it? – simmy Jan 12 '16 at 9:41
• McNeil & Frey paper is interesting. – noob2 Jan 12 '16 at 13:54