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We can compute VaR using Historical data and also by Fitting the tails of my Historical data to a GPD(Generalized Pareto Distribution) as shown in EVT and then compute EVT VaR from there.

What advantages and dis advantages will each method hold over the other?

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  • $\begingroup$ Have you been able to find / perform any further analysis on this? Any good papers that compare the two approaches? Thanks $\endgroup$ – Confounded May 16 at 18:23
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Historical only has the advantage of being easily computable, that's pretty much it. It only makes sense if you have lots and lots of observations as you observed basically everything (you hope) that can happen.

EVT can model the tail better but you are making a parametric assumption - so you need to say why you think GPD is suitable. So this gives a better estimate as long as the distributional assumption holds. If it doesn't really, than you commit (quite likely) a massive error.

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I will also add that calculating VaR and CVaR via EVT allows for a further analytical 'peek' into the tail. A dataset may only have 100 points to calculate those values but with EVT and Power Laws you could analytically calculate a 99.9999% VaR or CVaR rather than just a 99% VaR/CVaR from the data.

Additionally a bigger advantage is when compared to Monte Carlo methods, EVT can be much faster for finding VaR.

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