In the commodity market the Cost of Carry model is used to price the futures and forwards contracts based on the spot price of the traded asset. The cost of carry is all the costs to carry an asset from the present until a certain future period, those are the cost to finance the asset (the interest), the storage costs, the transportation cost, and the insurance costs.

The cost of carry model looks at the price of the future or forwardcontract as a function of the spot price and the cost of carry, this is shown in equation (1) below.

F_t=S(1+C_t)

Where Ft is the future price at maturity t, S is the spot price, and Ct is the cost to carry the asset until maturity t and is expressed as a percentage of the price.

The cost

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When the future prices are lower than what they should be according to the cost of carry model, the action of buying future contracts by arbitrageurs will put upward pressure on the price.

The cost of carry model can also be used to price the different future contracts, contracts on the same commodity but with different maturity dates. Equation (4) below represents such a model,

F_t=F_x (1+C_(t-x)) where Fx is the price of a future contract which will mature at x, and Ct-x is the cost of carry between the period t and x.

Just like the model looking at future prices in terms of spot prices, should the future price at maturity t not be equal to the future price at maturity x there will be arbitrage opportunities which when exploited will force the price into equilibrium.

Cost of Carry and Convenience Yield

Looking at the futures on commodities, a contrast should be made between the consumption and investment commodities. Investment commodities are assets held by a number of people only for investment purposes, while the consumption commodities are assets held by a number of people for primarily consumption

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The market for consumption commodities is different; owners of asset have a different view of holding an asset through a future’s contract than holding an asset in their inventory. It is some time to the advantage of the owner to hold the asset in his inventory; this benefit is expressed in the literature of commodities as the convenience yield.

The cost of carry model takes the convenience yield into account when there is a persistent difference in the price of a future and its spot price and the cost of carry (equation (1)). In equation 5 below, y represents the convenience yield and is meant to calculate the difference between the right hand side and the left hand side in equation 1.

F_t (1+y)=S(1+C_t) Equation (5)

Backwardation and Contango

The prices of futuresare to some extent reflections of the future spot prices on an asset. In fact, the model of future prices in terms of return is built upon the expected future spot price, rather than the actual spot price, as it is on the expected spot price that the investor will forecast his future profit. The model is represented by equation (6)