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AN ANALYTICAL SOLUTION FOR PARISIAN UP-AND-IN CALLS

Part of: Applications Mathematical finance

Published online by Cambridge University Press:  27 January 2016

NHAT-TAN LE Open the ORCID record for NHAT-TAN LE [Opens in a new window] ,
XIAOPING LU Open the ORCID record for XIAOPING LU [Opens in a new window]  and
SONG-PING ZHU Open the ORCID record for SONG-PING ZHU [Opens in a new window]
NHAT-TAN LE*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email ntl600@uowmail.edu.au, xplu@uow.edu.au, spz@uow.edu.au
XIAOPING LU
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email ntl600@uowmail.edu.au, xplu@uow.edu.au, spz@uow.edu.au
SONG-PING ZHU
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email ntl600@uowmail.edu.au, xplu@uow.edu.au, spz@uow.edu.au
*
✉ntl600@uowmail.edu.au
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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.

Keywords

Parisian options“moving window” techniqueanalytical solutionscoupled integral equations

MSC classification

Primary: 91G20: Derivative securities
Secondary: 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems) 62P05: Applications to actuarial sciences and financial mathematics

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 3 , January 2016 , pp. 269 - 279
Copyright
© 2016 Australian Mathematical Society 

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