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INTEGRAL EQUATION FORMULATION FOR SHOUT OPTIONS

Part of: Representations of solutions Mathematical finance

Published online by Cambridge University Press:  08 August 2018

R. MALLIER  and
J. GOARD Open the ORCID record for J. GOARD [Opens in a new window]
R. MALLIER
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada email rolandmallier@hotmail.com
J. GOARD*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, Australia email joanna@uow.edu.au
*
✉joanna@uow.edu.au
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Abstract

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We use an integral equation formulation approach to value shout options, which are exotic options giving an investor the ability to “shout” and lock in profits while retaining the right to benefit from potentially favourable movements in the underlying asset price. Mathematically, the valuation is a free boundary problem involving an optimal exercise boundary which marks the region between shouting and not shouting. We also find the behaviour of the optimal exercise boundary for one- and two-shout options close to expiry.

Keywords

shout optionsfree boundary problemsintegral equations

MSC classification

Primary: 91G20: Derivative securities
Secondary: 35C10: Series solutions
Type
Research Article
Information
The ANZIAM Journal , Volume 60 , Issue 1 , July 2018 , pp. 65 - 85
Copyright
© 2018 Australian Mathematical Society 

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