Loss function-based change point detection in risk measures

We propose a new test to detect change points in financial risk measures, based on the cumulative sum (CUSUM) procedure applied to the Wilcoxon statistic within a popular class of loss functions for risk measures. The proposed test efficiently captures change points jointly in two risk measure series: Value-at-Risk (VaR) and Expected Shortfall (ES), estimated by (semi)parametric models. We derive the asymptotic distribution of the proposed statistic and adopt a stationary bootstrapping technique to obtain the p-values of the test statistic. Monte Carlo simulation results show that our proposed test has better size control and higher power than the alternative tests under various change point scenarios. An empirical study of risk measures based on the S&P 500 index illustrates that our proposed test is able to detect change points that are consistent with well-known market events.