Why is the initial value of a forward contract set to zero?

Forward contracts are buy/sell agreements that specify the exchange of a specific asset and on a specific future date but on a price that is agreed upon today. They do not require early payment or down payment unlike some other future commitment derivative instruments. Since no money changes hands at the initial agreement, no value can be attributed to it. In other words, the forward price is equal to the delivery price.

Derivative valuation is not an exact science, and it is a subject of serious philosophical and methodological deviation between financial economists, security engineers and market mathematicians. The most common treatment of forward contracts begins with the assumed observation that forward contracts can be stored at zero cost. If a security can be stored at zero cost, then the forward price for delivery of the security is equal to the spot price divided by the discount factor.

You may see this expressed as: F = S / d(0,T), where (F) is equal to the forward price, (S) is the current spot price of the underlying asset, and d(0,T) is the discount factor for the time variable between the initial date and the delivery date.

The discount factor depends on the length of the forward contract. Mathematically, this is demonstrated as an equilibrium price because any forward price above or below this value represents an arbitrage opportunity.

At a date where (T) is equal to zero, the value of the forward contract is also zero. This creates two different but important values for the forward contract: forward price and forward value. Forward price always refers to the dollar price of assets as specified in the contract. This figure is fixed for every time period between the initial signing and the delivery date. The forward value begins at storage cost and tends toward the forward price as the contract approaches maturity.

What is the initial value of a $300,000 mortgage contract that requires a 15% down payment? Simple economic logic suggests the initial contract value is $45,000, or 0.15 x $300,000. That is how much money the lender demands to establish the contract. The borrower also agrees to part with $45,000 to receive the initial contract.

Carry this logic to forward contracts. The vast majority of forward contracts carry no down payment. If both parties are willing to exchange their commitment to the contract for $0.00, then it follows that the initial value of the contract is zero.

These explanations are incomplete, because they ignore many of the factors associated with mortgage and forward contracts, namely the underlying assets. However, in a strict economic sense, these arguments are valid.