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.

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    $\begingroup$ 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. $\endgroup$ – noob2 Jan 11 '16 at 18:51
  • $\begingroup$ 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? $\endgroup$ – simmy Jan 11 '16 at 20:17
  • $\begingroup$ 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. $\endgroup$ – noob2 Jan 11 '16 at 21:25
  • $\begingroup$ @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? $\endgroup$ – simmy Jan 12 '16 at 9:41
  • $\begingroup$ McNeil & Frey paper is interesting. $\endgroup$ – noob2 Jan 12 '16 at 13:54

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