A risky business: how to price derivatives

December 2008

A general formula for the multi-period case

The price for the option in an period model is given by

Here denotes the number of ways in which one can choose objects from a selection of objects (called the binomial coefficient — you can read more in the Plus article Making the grade: Part II). Explicitly it is given by where The symbol stands for with a subscript consisting of and - these stand for the payoffs corresponding to the various combinations of good and bad periods.
The expression means that you should sum the terms of the form in turn with substituted by 0, 1, 2, etc, up to .

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