The Risk Dependence Structure between the Futures and Spot Market -- A Mixture Copula Approach

In this paper, we investigate the risk dependence structure problem of the rate of return series in China stock market between Shanghai Shenzhen 300 index and the portfolio index of ETFs using mixture copula approach. The portfolio index of ETFs is formulated through a combination of Shanghai 180 ETF, Shanghai 50 ETF and Shenzhen 100 ETF. Five elementary copulas family are used to construct the mixture copulas. The relationship between the mixture copulas and their parents are compared. We find that there exists significant upper tail risk dependence for the two log-returns series to some extent. Our findings have important applications for arbitrage trading and financial risk management based on the stock index futures and the portfolio index of ETFs.