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AN ANALYTICAL SOLUTION FOR PARISIAN UP-AND-IN CALLS

Published online by Cambridge University Press:  27 January 2016

NHAT-TAN LE*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email [email protected], [email protected], [email protected]
XIAOPING LU
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email [email protected], [email protected], [email protected]
SONG-PING ZHU
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email [email protected], [email protected], [email protected]
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Abstract

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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.

Type
Research Article
Copyright
© 2016 Australian Mathematical Society 

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