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This is John Hull's book Options, Futures and Other Derivatives 9th Page 142

Suppose the maturity of a Eurodollar futures is $T.$

Then the settlement of futures is $T$ and the payment of deposit for the interest is $T+0.25?$

As this understanding, suppose enter rate of future is $F$ and the real rate of future is $P$ at $T.$ We would assume an interest rate of $F$ for the three-month period at time $T.$

Then we will receive the cash flow $(F-P)\times 0.25$ from futures settlement at $T$(suppose only pay one time at $T$) and receive the deposit of interest $P*0.25$ at $T+0.25,$ discounted the deposit into $T$ we have the total cash of $1$ contract $$(F-P)*0.25 +\dfrac{P*0.25}{1+F*0.25}.$$ To keep the the rate is still $F$ at $T,$ we should hold $k$ contract, then we have the equation $$\left((F-P)*0.25 +\dfrac{P*0.25}{1+F*0.25}\right)\times k = F.$$

I can not understand the result in the example $1/(1+0.035 * 0:25)= 0.9913$ contracts.

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The futures contract pays off every day during its life, with the last payment at T. There are no payments after that. When Hull is talking about a payment at T+.25 he is referring to the payoff of an investment that is separate from the futures contract.

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  • $\begingroup$ that means we receive the profit of futures at $T,$ meanwhile put the profit into the bank account to earn the interest with rate 0.035 and put the principle 1000000 into the Eurodollar account to earn the interest with rate 0.026. Up to $T + .25,$ we equivalently earn the interest on the principle 1000000 for $0.25$ year with rate $0.035?$ $\endgroup$ – A.Oreo Sep 16 '17 at 11:44
  • $\begingroup$ yes that is correct $\endgroup$ – dm63 Sep 16 '17 at 15:00

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