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Choosing Between Generalized Pareto and Cornish-Fisher VaR

Article Quant Q&A · Author: pmr
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Summary

The document considers two approaches to estimating Value at Risk: fitting a Generalized Pareto Distribution to extreme returns and calculating Modified Cornish-Fisher VaR. It asks whether one method is more accurate and mentions R packages that can implement these techniques, but offers no code or empirical comparison.

The response says suitability depends on the loss distribution. Cornish-Fisher estimates may be less accurate when returns depart substantially from normality, while a GPD approach can be useful for tail behavior but requires enough observations to estimate extremes reliably. The sample size concern is especially relevant to block maxima. Without inspecting the data, the discussion cannot identify a generally superior method; it also suggests a risk-management package associated with a quantitative risk management text as a resource.

Key ideas

  • VaR method performance depends on the distribution of losses in the data.
  • Modified Cornish-Fisher VaR may be less accurate when losses depart strongly from normality.
  • Generalized Pareto tail estimation requires sufficient observations to estimate extremes reliably.
  • The document provides no data-based test that determines which approach is more accurate for a particular portfolio.

Tags

Risk managementStatisticsVolatilityBacktesting
Full text
# VaR calculation accuracy/comparison/effectiveness through different R packages


# VaR calculation accuracy/comparison/effectiveness through different R packages












My question is what would be the better( in terms of estimation accuracy) method of VaR calculation among below two:, also any small code snippet will be great as a starting point for me.

1st method: I am trying to using a Generalized Pareto Distribution(GPD) there. I think R package POT or EVD might be of some help to fit my monthly historical return data to a GPD. Then using fExtremes package VaR might be calculated.

2nd Method : Another way is using PerformanceAnalytics package and trying calculate Modified Cornish-Fisher VaR.

## Answer by Kumar (score 0, accepted)

https://quant.stackexchange.com/a/18472

The results depend on your distribution of losses.

If there is lot of departure from Normality, Cornish-Fisher VaR results will not be as accurate as GPD. But again to estimate block maxima effectively you need a large amount of data.

So it is difficult to say much without looking at the data.

Also, I would use the QRM package that accompanies the book, "Quantitative Risk Management".

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