Research on the Dynamic Correlation Between the VIX Index and The Risk of Stock Market Crash

VIX index is closely related to stock market crash risk in depth. The VIX data from January 1, 2000 to 31 December 2020 were selected as well as the data related to the S&P 500 Index from January 1, 2000 to 31 December 2020, using literature research method, empirical analysis method (constructing multivariate linear regression model combined with GARCH-M model) and case analysis methods. According to descriptive statistics, the mean VIX index is 19.56 with a standard deviation of 9.87; the mean value of the stock market risk measure index (negative skewness index) is - 0.25, and standard deviation is 0.32. According to correlation analysis, Pearson correlation coefficient between VIX index and negative skewness index was 0.68, with a significant positive correlation of 1%. In regression results, a VIX regression coefficient of 0.08 is significantly positive at 1% significance level, i.e., for every 1 unit increase in the VIX index, the index increases 0.08 units. Robustness tests are used to test the robustness of the positive correlation by replacing variables with varying sample intervals. This study provides a key reference for investor risk management and regulatory policy making.