Employing the dataset of WTI oil spot price and stock price index in China􀀁Brazil, India, US, German, France, UK and Japan, this paper obtains five subinterval of whole sample range through a nonparametric multiple change point algorithms. Furthermore, it analyses dependence between oil spot price and stock price index through copula model and computes the value of VaR and ES based on simulation for every subinterval. It reveals that dependence between oil spot price and stock price index during financial crisis and there is asymmetric tail dependence. The value of VaR and ES of t oil spot price and stock price index shows irregular fluctuation.