A mixed data sampling copula model for the return-liquidity dependence in stock index futures markets

Understanding and quantifying the dependence of returns and liquidity is critical for liquidity risk management. In this paper the idea of mixed data sampling (MIDAS) is extended from linear correlation in Colacito et al. (2011) to the more general dependence measure: copula, and a copula-MIDAS model is proposed to describe the asymmetric return-liquidity dependence of CSI 300 index futures with short-run and long-run components. Based on the skewed t copula-MIDAS model, it is found that extreme decreases in returns tend to be accompanied by extreme increases in bid-ask spreads, but extreme increases in returns may not coincide with extreme reductions in bid-ask spreads. Furthermore, the return-spread dependence consists of both short-run and long-run components, and the long-run component will influence the return-spread dependence in the next two weeks. Last, the out-of-sample forecast of liquidity risk stresses the importance of considering asymmetry and long-run trend in return-spread dependence as it enables investors to well predict liquidity risk in times of market crashes. The results imply that high frequency trading investors of CSI 300 index futures should pay more attentions to prevent the potential liquidity risk when the bid-ask spreads are widened. And investors are suggested to use the past two-week high frequency data to forecast the current return-spread dependence in liquidity risk management.