Stochastic Finance, 4th Edition

5.6Exotic derivatives

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 ...