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Estimating the Variance of Bootstrapped Risk Measures

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  • Kim, Joseph H.T.
  • Hardy, Mary R.

Abstract

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.

Suggested Citation

  • Kim, Joseph H.T. & Hardy, Mary R., 2009. "Estimating the Variance of Bootstrapped Risk Measures," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 199-223, May.
    • Handle: RePEc:cup:astinb:v:39:y:2009:i:01:p:199-223_00
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    Cited by:

    1. Kim, Joseph H.T., 2010. "Bias correction for estimated distortion risk measure using the bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 198-205, October.
    2. Gao, Huan & Mamon, Rogemar & Liu, Xiaoming, 2017. "Risk measurement of a guaranteed annuity option under a stochastic modelling framework," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 100-119.
    3. Chen, Cong & Zhang, Su & Zhang, Guohui & Bogus, Susan M. & Valentin, Vanessa, 2014. "Discovering temporal and spatial patterns and characteristics of pavement distress condition data on major corridors in New Mexico," Journal of Transport Geography, Elsevier, vol. 38(C), pages 148-158.

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