Powerful Backtests for Historical Simulation Expected Shortfall Models
指出历史模拟和滤波历史模拟预期缺口模型的无条件回测在样本量大时效力甚至低于名义水平，并提出一类新的条件回测方法，通过蒙特卡洛模拟和股票指数数据验证了其优越性。
Since 2016, the Basel Committee on Banking Supervision has regulated banks to switch from a Value-at-Risk (VaR) to an Expected Shortfall (ES) approach to measuring the market risk and calculating the capital requirement. In the transition from VaR to ES, the major challenge faced by financial institutions is the lack of simple but powerful tools for evaluating ES forecasts (i.e., backtesting ES). This article first shows that the unconditional backtest is inconsistent in evaluating the most popular Historical Simulation (HS) and Filtered Historical Simulation (FHS) ES models, with power even less than the nominal level in large samples. To overcome this problem, we propose a new class of conditional backtests for ES that are powerful against a large class of alternatives. We establish the asymptotic properties of the tests, and investigate their finite sample performance through some Monte Carlo simulations. An empirical application to stock indices data highlights the merits of our method.