Pricing Futures

The pricing of futures is illustrated below with reference to (1) The Cost of Carry Model. (2) pricing equity index futures and (3) Pricing stock futures.

The Cost of Carry Model

The cost of carry model explains the dynamics of pricing that constitute the estimation of the fair value of futures. The fair value calculation of futures is used to decide the no arbitrage limits on the price of a future contract. According to this model using compounding, where interest rates are compounded at discrete intervals (for example, annually, semi-annually) the price of the contract is defined as:

F = S+ C
where F= Futures price
S = Spot price
C = Holdings costs or carry posts
This can also be expressed as:
F =  S (1 + r)T

To illustrate cost of carry, let us take an example of a futures contract on a commodity and work out the cost of contract. The spot price January 1, Year 1, of silver is assumed to be Rs 7,000/kg. Assuming an annual cost of financing of 15 per cent and no storage cost, the fair value of the future price of 100 gms of silver one month hence (January 30, Year 1) would be as follows:


If the contract is for a three month period expiring on March 30, Year 1, the cost of financing increase the future price, that is, F= Rs 700 (1.15) x 90/365 = Rs 724.5. If, however, the one month contract was for 10,000 kgs, it would involve storage cost and the price of the future
contract would be Rs 708 plus the cost of storage:

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