论文标题
在重尾巴下估计和进行回测风险
Estimating and backtesting risk under heavy tails
论文作者
论文摘要
尽管{估计}风险是银行和保险日常业务中的一个重要问题，但许多现有的插件估算程序都遭受了不必要的偏见。这通常会导致风险低估，并对回测结果产生负面影响，尤其是在小样本案例中。在本文中，我们表明，估计偏差与回测之间的联系可以追溯到风险度量和相应的绩效指标之间的双重关系，并参考危险价值，预期的不足和预期价值危险。通过插件程序对风险的一致低估，我们提出了一种新的偏差校正算法，并向I.I.D.设置和GARCH（1,1）时间序列。特别是，我们表明，当数据中存在沉重的尾巴或异方差，我们的算法的应用会导致效率提高。
While the {estimation} of risk is an important question in the daily business of banking and insurance, 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, expected shortfall and expectile value-at-risk. Motivated by the consistent underestimation of risk by plug-in procedures, we propose a new algorithm for bias correction and show how to apply it for generalized Pareto distributions to the i.i.d. setting and to a GARCH(1,1) time series. In particular, we show that the application of our algorithm leads to gain in efficiency when heavy tails or heteroscedasticity exists in the data.
