An analytical solution for Parisian up-and-in calls

Abstract

We derive an analytical solution for the value of Parisian up-and-in calls by using the ``moving window†technique for pricing European-style Parisian up-and-out calls. Our pricing formula can be applied to both European-style and American-style Parisian up-and-in calls, due to the fact that with an ``in†barrier, the option holder cannot do or decide on anything before the option is activated, and once the option is activated it is just a plain vanilla call, which could be of American style or European style. doi:10.1017/S1446181115000267