While the estimation of risk is an important question in the daily business of banks and insurances, it is surprising that efficient procedures for this task are not well studied. Indeed, many existing plug-in approaches for the estimation of risk suffer from an unnecessary bias which leads to the underestimation of risk and negatively impacts backtesting results, especially in the small sample environment . In this article , we consider efficient estimation of risk in practical situations and provide means to improve the accuracy of risk estimators and their performance in backtesting. In particular , we propose an algorithm for bias correction and show how to apply it for generalized Pareto distributions. Moreover, we propose new estimators for value-at-risk and expected shortfall , respectively, and illustrate the gain in efficiency when heavy tails exist in the data.
While the estimation of risk is an important question in the daily business of banks and insurances, many existing plug-in estimation procedures suffer from an unnecessary bias . This often leads to the underestimation of risk and negatively impacts backtesting results, especially in small sample cases . In this article we show that the link between estimation bias and backtesting can be traced back to the dual relationship between risk measures and the corresponding performance measures, and discuss this in reference to value-at-risk and expected shortfall frameworks. Motivated by this finding , we propose a new algorithm for bias correction and show how to apply it for generalized Pareto distributions. In particular, we consider value-at-risk and expected shortfall plug-in estimators, and show that the application of our algorithm leads to gain in efficiency when heavy tails exist in the data.
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