An analytical solution for Parisian up-and-in calls

Tan Nhat Le, Xiaoping Lu, Song-Ping Zhu


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.



Parisian options; ``moving window" technique; analytical solutions; coupled integral equations


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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.