Endogenizing Model Risk to Quantile Estimates

Carol Alexander and José María Sarabia ()

ICMA Centre Discussion Papers in Finance from Henley Business School, University of Reading

Abstract: We quantify and endogenize the model risk associated with quantile estimates using a maximum entropy distribution (MED) as benchmark. Moment-based MEDs cannot have heavy tails, however generalized beta generated distributions have attractive properties for popular applications of quantiles. These are MEDs under three simple constraints on the parameters that explicitly control tail weight and peakness. Model risk arises because analysts are constrained to use a model distribution that is not the MED. Then the model's alpha quantile differs from the alpha quantile of the MED so the tail probability under the MED associated with the model's alpha quantile is not alpha, it is a random variable. Model risk is endogenized by parameterizing the uncertainty about this random variable, whence the model's alpha quantile becomes a generated random variable. To obtain a point model-risk-adjusted quantile, the generated distribution is used to adjust the model's alpha quantile for any systematic bias and uncertainty due to model risk. An illustration based on Value-at-Risk (VaR) computes a model-risk-adjusted VaR for risk capital reserves which encompass both portfolio and VaR model risk.

Keywords: Quantile risk measures; model risk; maximum entropy; generalized beta normal (GBN) distributions; generalized beta generated (GBG) distributions; Value-at-Risk (VaR); risk capital; S&P 500 index; GARCH; RiskMetrics (search for similar items in EconPapers)
JEL-codes: C1 C19 C51 G17 G28 (search for similar items in EconPapers)
Date: 2010-07
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.icmacentre.ac.uk/files/discussion-papers/dp201007.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (http://www.icmacentre.ac.uk/files/discussion-papers/dp201007.pdf [302 Found]--> https://www.icmacentre.ac.uk/files/discussion-papers/dp201007.pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:rdg:icmadp:icma-dp2010-07

Access Statistics for this paper

More papers in ICMA Centre Discussion Papers in Finance from Henley Business School, University of Reading Contact information at EDIRC.
Bibliographic data for series maintained by Marie Pearson ().