Integral equation formulation for shout options

Roland Mallier, Joanna Goard

Abstract


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.



doi:10.1017/S1446181118000160

Keywords


shout options, free boundary problems, integral equations.



DOI: http://dx.doi.org/10.21914/anziamj.v60i0.12258



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