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Comparing Historical VaR with EVT Tail Extrapolation

Article Quant Q&A · Author: Deb
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Summary

Historical Value at Risk uses observed returns directly, making it simple to calculate. Its weakness is that reliable estimates depend on having enough observations to capture the range of losses that may occur; limited samples cannot reveal every possible tail event.

Extreme Value Theory fits a Generalized Pareto Distribution to historical tail observations to estimate extreme VaR or conditional VaR beyond the sample quantiles. This can provide estimates at more extreme confidence levels and may be faster than Monte Carlo methods. The benefit depends on the tail model being appropriate: the parametric assumption must be justified, since a poor fit can produce large errors. The discussion gives conceptual comparisons but no empirical test of either method.

Key ideas

  • Historical VaR is straightforward to compute but depends on a large sample to represent rare losses.
  • EVT fits a Generalized Pareto Distribution to tail data to extrapolate beyond observed quantiles.
  • EVT estimates are useful only when the chosen tail distribution fits the data adequately.
  • The discussion notes that EVT can be faster than Monte Carlo for VaR estimation.

Tags

StatisticsRisk managementVolatility
Full text
# Historical VaR vs. EVT VaR


# Historical VaR vs. EVT VaR












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?

## Answer by Jan Sila (score 3, accepted)

https://quant.stackexchange.com/a/30027

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.

## Answer by salisboss (score 3)

https://quant.stackexchange.com/a/30034

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.