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The stock index futures price must converge with the spot index price on the maturity date. Why?
I think so too. There must be convergence in theory, so there must be so-called risk-free arbitrage in theory. But for example, if you take a two-way position, occupation cost may be higher than your risk-free income, and besides the relatively homogeneous target such as bonds, the quality of the spot will affect the final delivery.