Forward Contract: Agreement to buy or sell an asset at a certain time for a certain price. Traded usually between two financial institutions. One of the parties has a long position who agrees to buy the underlying asset at a certain price, the party who holds the short position agrees to sell the asset at a certain price on the same date. The price in the forward contract is called the delivery price. It is adjusted so that at the time of the contract the value of the forward contract is zero to both sides.

If we assume the price of the asset at maturity ( ending time of the contract) as St then the payoff of the forward contract for the long position is St-K, and the payoff for the short position is K-St, where K is the delivery price.

Example 1: You know that you will get 1 million Dollar 3 months later, you go into a 3 month forward contract whose exchange rate (delivery price) on TL is 700,000. that means you will sell 1 million dollar with that exchange rate to the other party for 1million * 700,000 TL.

Forward price of a particular forward contract at a particular time is the delivery price that would be applied if the forward contract were entered at that time. So at the initial delivery price and forward price are same but later they change. In the example 700,000 is both  the delivery price and forward price at the beginning. But one month later the forward price with a maturity of 2 months maybe different from the delivery price which is still 700,000. Suppose the 3 month forward contract starts in January and ends at the end of march. Initially the forward price and delivery price are same and they are 700,000. but in February to enter into a forward contract that will end at the end of march is different from 700,000 because then the exchange rates would be different from the exchange rates of the January.

Example 2: Suppose the price of gold is 300$/ounce and the risk free rate (the rate that you get when you deposit your money in the bank) is 5% annually. What should be the one-year forward price of gold?

Answer:  Lets start with a price and see what happens. Lets say that the one year forward  price is 340$/ounce. Then I can do this I borrow 300$ from the bank, go into the contract and hold a short position, at the end of the year sell the gold for 340$ and give 315$ (300+300*5%) to the bank and you get profit of 25$. This is explicitly an arbitrage opportunity. If the forward price was 315$, you would not have such a chance. So the fair price is 315$.

Futures Contract: It is the same with forward contract but the only difference is that it is traded on an exchange. It has standards. The delivery date is not specified usually. It may be entire month.