so the formula for the value of a forward is f = S - Ke^-(rt) where S is the spot price
assuming the spot price doesn't move, why does it make sense that the value of the forward should decline over time? or is it just that the implicit assumption in pricing a forward that the spot price will increase at the riskless rate, so that when it doesn't happen, the price of the forward declines?
Time value of money
The spot will increase in value. Its easier to think about it as 0= S- F/(1+r)^t. The idea is that you are indifferent between investing in the spot today, or buying the item's future/forward today and investing the money that would have been spent on the good spot at the risk free rate. Of course this equation only holds at t=0, to find the value of the forward after it has been purchased, keep f constant, and adjust the spot price, r and t (time to maturity of the forward contract). This is arbitrage free price as long as the right hand side of the equation is equal to 0. If it wasnt, you could make an arbitrage profit by going either long spot and short in the forwards market or vice versa depending upon the mispricing.
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