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At the very least we know that both do not want to lose any money in the deal. So of course they will have to settle on a fair price or else the transaction cannot occur. 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. 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. See Musiela and Rutkowski’s book on Martingale Methods in Financial Markets for a continuous-time proof of this result. See van der Hoek and Elliott’s book on Binomial Models in Finance for the discrete-time version of this result. When you login to the binary robot, you can choose your own settings and aim to achieve similar results as the users below.
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