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Given we understand forward contract precisely with term structure of risk free rates, do we understand futures contracts as a continuous buying and selling sequences of forward contracts so that the forward contracts always worth 0 on my account?

My attempt:

Reading through and integrating the understanding of term structure of interest rates.

https://faculty.weatherhead.case.edu/ritchken/textbook/Powerpoint/Notes2.PDF

I think we can understand futures contracts roughly as a continuous buying and selling sequences of forward contracts so that the forward contracts always worth 0 on my account. However, the position corresponding to forward contracts are (slightly) larger at the beginning based on the interest rates term structure Psi(t,T) and such position converge to 1 in the end. However, due to the correlation between interest rates and underlying, one probably cannot exactly replicate Futures from Forwards.

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