Vol. LXXX, 1 (2011)
p. 79 - 102

Laplace transforms and shout options

G. Alobaidi, R. Mallier and S. Mansi

Received: April 18, 2010;   Revised: September 27, 2010;   Accepted: October 3, 2010

Abstract.   We use Laplace transform methods to examine the optimal exercise boundary for shout options, which give the holder the right to lock in the profit to date while retaining the right to benefit from any further upside. The result of our analysis is an integro-differential equation for the location of this optimal exercise boundary. This equation is a nonlinear Fredholm equation, or more specifically, an Urysohn equation of the first kind. Applying an inverse Laplace transform to this equation allows us to find the behavior of the free boundary close to expiry. The results are given for both call and put shout options.

Keywords:  American options; shout options; integro-differential equations; Laplace transforms  

AMS Subject classification: Primary:  44A10, 45G10  

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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

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