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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