An Intraday Time-Point Co-Jump Test Method Based On Local Volatility Estimation

The co-jump test method is an important method in the field of financial econometric.In 2008,Bollerslev,Law and Tauchen(2008)first proposed a multi-asset price co-jump test method(BLT test)for time points.In 2014,Gnabo,Hvozdyk and Lahaye(2014)based on the BLT test for two asset scenarios.The parameter estimation method is improved,and a mechanism to prevent the single-hop error from being recognized as a co-jump(GHL test)is designed.However,the above methods have an important assumption that the intraday volatility(diffusion coefficient)is constant.In this paper,Monte Carlo method is used to simulate the scene with variable intraday volatility,and the performance of BLT test and GHL test are compared in the random volatility scenario.It is found that the GHL test performs better than the BLT test in the scenario of two assets with random volatility,but the GHL test method is still based on constant intraday volatility,which is different from the simulated intraday volatility variable scenario.For the stochastic volatility scenarios with variable intraday volatility,based on the BLT test and GHL test,we propose a local volatility estimation method based on Lee and Mykland(2008)time point single-jump test,called stochastic volatility GHL test(SVGHL).The innovation of this method is to relax the assumption that the intraday volatility is constant,and use the local lag information to estimate the volatility,so that the intraday volatility of the asset can be time-varying.Comparative analysis of BLT,GHL,and SVGHL tests was performed by Monte Carlo simulation.Taking the nominal significance level of 5%,it was found that the SVGHL test was more capable of recognizing the co-jump than the BLT test and the GHL test,that is,the SVGHL test had the greatest power,and the test size of the SVGHL test was closer to the nominal significance level of 5%.When there is only one sequence jump,if the jump is large,the test level of the SVGHL test is closest to 5%.The SVGHL test has a test size slightly above 5%when there is no jump in both sequences.Finally,this paper uses the five-minute high-frequency data of China's Shanghai Stock Exchange Index and the Shanghai and Shenzhen 300 Index,the National Debt Index and the Shanghai and Shenzhen 300 Index to compare the test results of BLT test,GHL test and SVGHL test.It is found that the co-jump recognition ability of the GHL test is stronger than the BLT test.The co-jump recognition ability of the SVGHL test is stronger than the BLT test and the GHL test,which is consistent with the Monte Carlo analysis result of this paper.