A forward contract is a non-standardized contract between two parties to buy or to sell an asset at a specified future time at a price agreed upon today.
The price of a forward contract is the price specified in the contract at which the long and short sides have agreed to trade the underlying asset when the contract expires.
The value of a forward contract to each side is the amount of money the counterparty would be willing to pay (or receive) to terminate the contract. Its a zero-sum game, so the value of the long position is equal to the negative of the value of the short position.
The no-arbitrage price of the forward contract (with a maturity of T years) is the price at which the value of the long side and the value of the short side are both equal to zero.
The value of the short position at any point in time is the negative of the long position.