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In this article we look to introduce an 'fair' pricing method for future and forward contracts.  Due to the similar nature of the forward and future contracts, the pricing method employed for these two products is essentially the same.  Pricing forwards and future is much simpler than that for options since all the hedging is done at the beginning of the contracts.

Future and forward contracts do not have a premium that is paid to the either partly like the writer of an options, since both parties are exposed (locked) to the same level of risk.  Decisions to enter a future/forward contract can be based upon one's opinion of market movement, or even purely for hedging purposes.  As with other derivative products a 'sensible' method of pricing is to use the arbitrage argument - meaning we have to discount the present value S(t) at time t to maturity T by the rate of risk-free return r.  Thus, the value F(t) of the future/forward will be

This provides us with a reliable pricing scheme for a non-dividend paying asset.  If the asset is a share of a company (or better still a bond) with dividend yield we replace r by as we do with an option.  All we have done here is to account for the risk-free return on a asset to eliminate any arbitrage opportunities as done so in the framework of the Black-Scholes pricing.

For example, if our asset S(t) is money agreed to recieve at time T, this is similar to borrowing money from the bank at the risk-free interest rate.

Written by Alessio Farhadi

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