As financial derivative products and systemic risk management tools, stock index futures and options have been greatly developed and widely issued in many countries. Taking the Shanghai Stock Exchange 50 (SSE 50) Index and its derivatives as the research objects, we first analyze the lead–lag relationship between stock index, index futures and index options in the Chinese mainland stock market based on a thermal optimal path (TOP) method whose essence is a non-parametric methodology, and compare the results with two mature markets, namely the Hong Kong and US stock markets. We find: (I) In US and Hong Kong stock markets, the index future leads the index. The index option leads the index future when the index remains stable or in an up-trend, but their lead–lag relation reverses when the index collapses; (II) In the Chinese mainland stock market, the index leads the index future, and the index option leads the index future in the whole period of our investigation; (III) In all three markets, the index option leads the index when the index remains stable or in an up-trend, but their lead–lag relation reverses when the index collapses. Our work gives new and strong evidence that the lead–lag relationship varies in different markets and with different market conditions, which has an important contribution to the reveal of the price discovery function of derivative products.