Using GARCH and Value-at-Risk as Complementary Risk Measures

Summary

The document asks whether multiple risk estimators can be considered together, including whether their divergence might be summarized with a ratio or whether their correlation makes this redundant. The response suggests using GARCH and Value-at-Risk (VaR) in complementary roles, rather than treating them as interchangeable estimates or proposing a particular combined statistic.

It notes that the respondent does not know of a top finance journal paper using this combination, while pointing to related work in field journals. The cited finding is that stationary and fractionally integrated GARCH models outperform RiskMetrics when estimating 1% VaR. This provides a narrow example of comparing volatility-model approaches in a VaR application; it does not establish a general method for combining risk measures or quantify how much information they share. The discussion is brief and gives no details of the cited study’s data, testing design, or limits, so its result should not be generalized beyond that reported comparison.

Key ideas

• GARCH and VaR may be used as complementary risk concepts.
• The response does not propose a ratio or formula for measuring divergence between estimators.
• A cited study reports improved 1% VaR estimation from stationary and fractionally integrated GARCH models relative to RiskMetrics.
• The discussion provides no study details sufficient to assess how broadly that result applies.

Tags

# Ratios or combinations of risk measures


# Ratios or combinations of risk measures












In finance, alternative risk measures such as value-at-risk (VaR) and GARCH are introduced as replacements to standard deviation volatility.

Is there any application or value where several risk estimators or two are considered simultaneously? As an example, a ratio that describes the divergence between one another? Or are alternative risk measures just too correlated that that would be redundant

## Answer by phdstudent (score 1)

https://quant.stackexchange.com/a/55112

You can use Garch and VaR in complementary terms. I do not know of any top finance journal paper where that was done (as it is probably something not very novel). However, some field journals do have some interesting things on relating Garch and Value-at-Risk.

For example this paper states:

> The results indicate that both stationary and fractionally integrated GARCH models outperform RiskMetrics in estimating 1% VaR.

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