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Sir is there any relationship between lock-in rate, futures opening price and futures closing price? I know the traditional formula of lock in rate(=opening futures price + unexpired basis) but what am curious to know is a formula that includes closing futures rate too(especially when spot rate at the expiry is unknown)?
No there is not.
The lock-in rate when applied to the amount of the transaction gives the same amount as the net result of converting the transaction at whatever the spot turns out to be together with the gain or loss on the futures deal.
As the spot rate changes at the date of the transaction then so to the futures price at that date will change. Because the difference between the two – the basis – can be calculated in advance (due to our assumption that it falls linearly over the life of the future) we can forecast what the net effect will be, and this is given by the lock-in rate.
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