The lead–lag relationship between stock index and stock index futures: A thermal optimal path method

The study of lead–lag relationship between stock index and stock index futures is of great importance for its wide application in hedging and portfolio investments. Previous works mainly use conventional methods like Granger causality test, GARCH model and error correction model, and focus on the causality relation between the index and futures in a certain period. By using a non-parametric approach—thermal optimal path (TOP) method, we study the lead–lag relationship between China Securities Index 300 (CSI 300), Hang Seng Index (HSI), Standard and Poor 500 (S&P 500) Index and their associated futures to reveal the variance of their relationship over time. Our finding shows evidence of pronounced futures leadership for well established index futures, namely HSI and S&P 500 index futures, while index of developing market like CSI 300 has pronounced leadership. We offer an explanation based on the measure of an indicator which quantifies the differences between spot and futures prices for the surge of lead–lag function. Our results provide new perspectives for the understanding of the dynamical evolution of lead–lag relationship between stock index and stock index futures, which is valuable for the study of market efficiency and its applications.