The recursion formula (5.29) can be used for the numeric computation of the value process of any contingent claim. For the value processes of certain exotic derivatives which depend on the maximum of the stock price, it is even possible to obtain simple closed-form solutions if we make the additional assumption that
In this case, the price process of the risky asset is of the form
where, for Yk as in (5.25),
Let ℙ denote the ...