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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