With the global economic integration, the risk contagion between the economies is more significant, and the test of the infection effect becomes very important. In this paper, the traditional method of crisis contagion based on linear cointegration is generalized. Based on the quantile regression method, this paper makes an empirical study on the international stock market from the perspective of risk. Using nonlinear unit root test, it is proved that the daily spread of the standard & Poor's index and several other countries' stock index returns are not satisfied with the assumption of normality, so the application of quantile regression model is used to study the relationship between stock market volatility in the United States and the stock market volatility in different countries at different quantile. In this paper, we analyze the impact of the crisis on the stock market by comparing the cointegration coefficients in crisis and before the crisis to test the crisis contagion.
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