I don't fully understand Futures & Forward pricing. I know that there is a delivery price and the actual future price. And that at the time of issuing, the future price is identical to the delivery price.
From my textbook, I have that the future price
F_0 is given by
S_0 is the spot price. So, at issuance, the delivery price would be
So, should I buy the contract, I would receive the underlying at expiry T having paid
Now let's suppose that time passes, and the future price has increased. I now decide to buy the contract at time
t1 and we have that
F_0 is different from
When the contract expires, I simply receive the asset from the contract which I have payed
F_t1. So, where does the delivery price come into play?
If it doesn't, wouldn't the correct definition of a future contract be 'a legal agreement to buy or sell a particular commodity asset, or security at a specified time in the future' instead of 'a legal agreement to buy or sell a particular commodity asset, or security at a predetermined price at a specified time in the future'