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Which method apart from the cost of carry model exists, and which works best in real life? How does the market expectations impact on the futures price?

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When the required conditions are fulfilled ( a storeable commodity, an observable spot price, no "convenience yield") the cost of carry model determines the futures price by arbitrage.

Otherwise, to my knowledge, there is no alternative model. The futures price will just be the market's expectation (possibly plus or minus a risk premium) of what the commodity will be worth at the delivery date. In other words it can be just about anything in that case.

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    $\begingroup$ Take the example of a STIR (short term interest rate) future. There is no cost of carry since there is no asset to purchase and hold. The futures price is simply the market expectation of the publication of an index at a point in the future (as determined through analysis and no (practical) arbitrage measured against other similar products e.g. IRSs, FRAs etc.) $\endgroup$ – Attack68 Jan 23 at 21:31

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