A forward contract has no value at the time it is first entered into (i.e., its net present value is zero). However, as the contract advances in time, it may acquire a positive or negative value. Therefore, it would be financially much better to mark the contract to market, i.e., to value it every day during its life. The value of a long forward contract can be calculated using the following formula:
f = (F0 – K) e -r.T
where:
f is the current value of forward contract
F0 is the forward price agreed upon today, F0= S0. er.T
K is the delivery price for a contract negotiated some time ago
r is the risk-free interest rate applicable to the life of forward contract or a respective period within
T is the delivery date
S0 is the spot price of underlying asset
In the same token, the value of a short forward contract is given by:
f = (K – F0). e -r.T
For example, suppose a long forward contract on a non-dividend-paying stock (current stock price= $50) which has currently 3 months left to maturity. If the delivery price is $47, and the risk-free interest rate is 5%, then the value of this contract can be calculated in two steps:
First, we find the forward price (i.e. the 3-month forward price):
F0 = 50 x e0.05×3/12 = 50.63
Then, we plug this price along with the above information in the formula of long forward contract value:
f = ( 50.63 – 47) e-0.05×3/12 = 3.63 x 0.9876 = $ 3.585
