In this study, using Copula models to fit dependence structure between two indices, including Taiwan Weighted Stock Index, S&P 500 index, NASDAQ index, Shanghai Composite Index, Nikkei 225 Index and Korea Composite Index. Then using Lehman’s announcement of bankruptcy and PIIGS credit rating downgraded Day as a dividing point to divide into pre- and post. Through the fitting Copula to measure the correlation between two index returns, in order to facilitate investors gain on the index futures in these markets. Finally, we plot the contours of joint probability by risk probability plot method. Through the distribution of data, we can predict the probability of loss, and as a reference in investment decisions and the hedging strategy. According to the result, overall we can use Student-t copula to describe the dependent structure between two stock index returns. But when important events occur, Gumbel copula or Clayton copula is more suitable for fitting short-term return rate change. Finally, we use risk probability plot to measure the degree of the risk probability between stock index returns in different status.
