Empirical likelihood for value-at-risk and expected shortfall

Rafet Evren Baysal and Jeremy Staum

Journal of Risk

Abstract: ABSTRACT When estimating risk measures, whether from historical data or by Monte Carlo simulation, it is helpful to have confidence intervals that provide information about statistical uncertainty. We provide asymptotically valid confidence intervals and confidence regions involving value-at-risk (VaR), conditional tail expectation and expected shortfall (conditional VaR), based on three different methodologies. One is an extension of previous work based on robust statistics, the second is a straightforward application of bootstrapping, and we derive the third using empirical likelihood. We then evaluate the small-sample coverage of the confidence intervals and regions in simulation experiments using financial examples. We find that the coverage probabilities are approximately nominal for large sample sizes, but are noticeably low when sample sizes are too small (roughly, less than 500 here). The new empirical likelihood method provides the highest coverage at moderate sample sizes in these experiments.

References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.risk.net/journal-risk/2161031/empirica ... d-expected-shortfall (text/html)

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:rsk:journ4:2161031

Access Statistics for this article

More articles in Journal of Risk from Journal of Risk
Bibliographic data for series maintained by Thomas Paine (maintainer@infopro-digital.com).