The linear and nonlinear lead–lag relationship among three SSE 50 Index markets: The index futures, 50ETF spot and options markets

Abstract The lead–lag relationship in finance markets has always been the focus point of many researches. The linear Granger causality, a classic method for the research of lead–lag relationship, has been extensively analyzed for markets of spot, future and option, but the nonlinear causality between spot and option markets has attracted little attention. This article first analyzes the linear and nonlinear Granger Causality among Shanghai Stock Exchange 50 (SSE 50) index futures, SSE 50ETF spot and options markets, and compares the effects of different time frequencies on test results. From the results of Granger causality test, we demonstrate some significant lead–lag relationships via 1-hour data, whereas the 5-minutes data may be detrimental to nonparametric Granger causality test. Furthermore, from the 1-minute data, we find that within one day, some different short-term lead–lag relationships appear, and they often contradict to the directions obtained from entire sample spanning 1 year. In search of the more detailed volatile causalities, we employ the nonparametric thermal optimal path (TOP) method on 5-minutes data, finding it potentially an expansion to the traditional Granger method, due to its ability to process high frequency data.