Estimating the variance of bootstrapped Risk measures

Joseph H.T. Kim, Mary R. Hardy

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


In Kim and Hardy (2007) the exact bootstrap was used to estimate certain risk measures including Value at Risk and the Conditional Tail Expectation. In this paper we continue this work by deriving the influence function of the exact-bootstrapped quantile risk measure. We can use the influence function to estimate the variance of the exact-bootstrap risk measure. We then extend the result to the L-estimator class, which includes the conditional tail expectation risk measure. The resulting formula provides an alternative way to estimate the variance of the bootstrapped risk measures, or the whole L-estimator class in an analytic form. A simulation study shows that this new method is comparable to the ordinary resampling-based bootstrap method, with the advantages of an analytic approach.

Original languageEnglish
Pages (from-to)199-223
Number of pages25
JournalASTIN Bulletin
Issue number1
Publication statusPublished - 2009

All Science Journal Classification (ASJC) codes

  • Accounting
  • Finance
  • Economics and Econometrics


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