opportunity cost of keeping the asset for that time period (he could have sold it and invested the money at the risk-free rate). let K = fair price C = cost of capital S = spot price of asset F = future value of asset's dividend I = present value of F (discounted using r ) r = risk-free interest rate compounded continuously T = length of time from when the contract was entered into Solving for fair price and substituting mathematics we get: where: (since where j is the effective rate of interest per time period of T ) where ci is the ith dividend paid at time t i. Doing some reduction we end up with: Notice that implicit in the above derivation is the assumption that the underlying can be traded. This assumption does not hold for certain kinds of forwards. Forward versus futures prices There is a difference between forward and futures prices when interest rates are stochastic. This difference disappears when interest rates are deterministic. In the language of stochastic processes, the forward price is a martingale under the forward measure, whereas the futures price is a martingale under the risk-neutral measure. The forward measure and the risk neutral measure are the same when interest rates are deterministic. See also Forward rate Forward measure Convenience yield Cost of carry Backwardation Contango References Bibliography Binomial Models in Finance - van der Hoek & Elliott Martingale Methods in Financial Markets - Musiela & Rutkowski Derivatives (finance) Financial economics