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Based on daily and one-minute high-frequency returns, this paper examines the lead–lag dependence between the CSI 300 index spot and futures markets from 2010 to 2014. A nonparametric and non-linear method based on the thermal optimal path method is adopted. Empirical results of the daily data indicate that the lead–lag relationship between the two markets is within one day but this relationship is volatile since neither of the two possible situations (the futures leads or lags behind the spot market) takes a dominant place. Our results using the high-frequency data demonstrate that there is a price discovery in the Chinese futures market: the intraday one-minute futures return leads the cash return by 0–5 min regardless of the price trend of the market. [ABSTRACT FROM PUBLISHER]