Calculating GED Quantiles for Parametric Value at Risk

Summary

The document gives a brief approach to calculating parametric Value at Risk when returns are modeled with a generalized error distribution (GED). It points to the GED quantile function in R’s fGarch package, with parameters for probability, mean, standard deviation, and shape. The selected lower-tail quantile can be used as a loss threshold under the assumed distribution.

The example uses a one-percent tail probability and illustrative distribution parameters, and the note describes the complement of that probability as the confidence level. It does not explain how to estimate GED parameters from GARCH residuals, how to align the quantile with a particular forecast horizon, or how to validate the resulting VaR. The calculation is therefore a distributional component of a VaR workflow rather than a complete risk model.

Key ideas

• A GED quantile can provide the tail cutoff for parametric Value at Risk.
• The R fGarch package supplies a quantile function with location, scale, and shape inputs.
• The tail probability and the reported confidence level are complements.
• A quantile calculation alone does not estimate or validate the full GARCH VaR model.

Tags

# How do I get Value-at-Risk for a GED distribution in R?


# How do I get Value-at-Risk for a GED distribution in R?












I need to calculate parametric Value-at-Risk using a GARCH model assuming a GED distribution. How can calculate it in R? thank you

## Answer by Neeraj (score 1)

https://quant.stackexchange.com/a/24795

### VaR for GED in R

```
package(fGarch)
qged(p, mean = 0, sd = 1, nu = 2)

#Example
qged(.01, mean=1000, sd=2000)
[1] -3652.696
```

where, $1-p$ is confidence level.

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