4.3 Futuresandfuturesoptions 4.3.1 Forwardcontracts Recall that a forward contract is an agreement between two parties to buy or sell an underlying asset on a certain price E at a certain future time T. Here, E is called the delivery price. The payoff function for this forward contract is Λ = ST − E. Based on the no arbitrage opportunity, the price for this forward contract is f = S−Ee−r(T−t). Definition3.2 The forward price F for a forward contract is defined to be the delivery price which would make that contract have zero value, i.e., Ft = Ster(T−t).
One can take another point of view. Consider a party who is short the contract. He can borrow an amount of money St at time t to buy an asset and use it to close his short position at T. The money he received at expiry, F, is used to pay the loan. If no arbitrage opportunities, then F = Ster(T−t).