On the Location of a Free Boundary for American Options

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dc.contributor.author Katende, Ronald J.
dc.date.accessioned 2018-02-12T08:42:43Z
dc.date.available 2018-02-12T08:42:43Z
dc.date.issued 2018-02-12
dc.identifier.citation Katende, 2017. en_US
dc.identifier.uri http://hdl.handle.net/123456789/4012
dc.description Master of Science in Mathematics (Financial Option) en_US
dc.description.abstract We study the free boundary problem of the American type of options. We consider a continuous dividend paying put option and provide much simpler way of approximating the option payo and value. The essence of this study is to apply geometric techniques to approximate option values in the exercise boundary. This, being done with the nature of the exercise boundary in mind, more accurate results are guaranteed. We de ne a transformation (map) from a unit square to the free boundary. We then examine the transformation and its properties. We take a linear case for a transformation as well as a nonlinear case which would be more tting for option values. We consider stochasticity (an Ito process) as we de ne this transformation and this yields better approximations for option values and payo s. We also numerically compute optimal option prices using the same transformation. We nally demonstrate that our transformation performs better than most semi-analytic results. en_US
dc.description.sponsorship Prof. Diaraf SECK Departement de Mathematiques de la Decision, Universite Cheikh Anta Diop, BP 16 889 Dakar-Fann Senegal Dr. Philip Ngare School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Kenya en_US
dc.language.iso en en_US
dc.publisher JKUAT-PAUSTI en_US
dc.subject Free Boundary en_US
dc.subject American Options en_US
dc.subject Financial Mathematics en_US
dc.title On the Location of a Free Boundary for American Options en_US
dc.type Thesis en_US

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