Journal of Computational Finance

A simple and robust approach for expected shortfall estimation

Zhibin Pan, Tao Pang and Yang Zhao

  • Propose a tail-based normal approximation for ES estimation.
  • Develop an adjusted tail-based normal ES estimation approach for heavy-tailed distributions.
  • The approach is easy to implement and robust for various heavy-tailed distributions.
  • The approach is substantially accurate and works well for small samples.

In risk management, estimating expected shortfall, though important and indispensable, is difficult when the sample size is small. This paper suggests a recipe for meeting such a challenge. A tail-based normal approximation with explicit formulas is derived by matching a specific quantile and the mean excess square of the sample observations. To enhance the estimation accuracy, we propose an adjusted tail-based normal approximation based on the sample's tail weight. The adjusted expected shortfall estimator is robust and efficient in the sense that it can be applied to various heavy-tailed distributions, such as Student t, lognormal, Gamma and Weibull, and the errors are all small. Moreover, compared with two common expected shortfall estimators -- the arithmetic average of excessive losses and extreme value theory estimator -- the proposed estimator achieves smaller mean squared errors for small samples, especially at high confidence levels. The properties of linear transformations on the expected shortfall estimator are also investigated to ensure its practicality.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to View our subscription options

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here