An analytical solution for Parisian up-and-in calls

Tan Nhat Le, Xiaoping Lu, Song-Ping Zhu

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

Keywords


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



DOI: http://dx.doi.org/10.21914/anziamj.v57i0.9046



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