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I just watched https://institute.cmegroup.com/courses/introduction-to-eurodollars/modules/understanding-convexity-bias

as I understand it, if the yield rate of a futures contract increases, the price changes linearly. However, with a forward contract the price is a function of the current yield as well as the change in yield?

Why is this the case?

EDIT:

from the link:

It is thought that the Convexity bias is due to the following:

1) The way Eurodollar futures are margined versus an FRA instrument

2) The cash flows paid out over the life of a futures contract versus an FRA. Futures are marked-to-market each day by the clearinghouse, while cash flows in an FRA are paid off differently.

3) Volatility in the interest rate markets, generally increasing volatility could cause margin changes.

But these are conjecture. Is there any concrete reason, or theoretical proof to this difference?

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