IDEAS home Printed from https://ideas.repec.org/a/rsk/journ4/5388396.html
   My bibliography  Save this article

Estimation risk for value-at-risk and expected shortfall

Author

Listed:
  • Paul Kabaila
  • Rheanna Mainzer

Abstract

For a given time series of daily losses that display volatility clustering, the exact next- day and ten-day value-at-risk (VaR) and expected shortfall (ES) are unknown. The usual procedure is to approximate these values by replacing true parameter values with estimates in the formulas for VaR and ES. Parameter estimation errors for a GARCH(1,1) model for this time series lead to approximate VaR and ES that differ from the exact VaR and ES, respectively. Accurate estimation of the VaR and ES is very important for the proper management of financial risks. In this paper, we find linear regression models in which the response variable is the approximate VaR (ES) and the explanatory variable is the exact VaR (ES). We use these linear regression models to determine the properties of the approximate VaR (ES), conditional on the corresponding exact value. For a given value of the exact VaR (ES), the approximate VaR (ES) is close to being an unbiased estimator of the corresponding exact value, but it may differ from this exact value by more than 10% of the exact value with substantial probability.

Suggested Citation

Handle: RePEc:rsk:journ4:5388396
as

Download full text from publisher

File URL: https://www.risk.net/system/files/digital_asset/2018-02/Estimation_risk_for_VaR_and_ES.pdf
Download Restriction: no
---><---

More about this item

Statistics

Access and download statistics

Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:rsk:journ4:5388396. See general information about how to correct material in RePEc.

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

We have no bibliographic references for this item. You can help adding them by using this form .

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thomas Paine (email available below). General contact details of provider: https://www.risk.net/journal-of-risk .

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.