文章基本信息

标题：On the Location of a Free Boundary for American Options
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作者：Ronald Katende ; Diaraf Seck ; Philip Ngare 等
期刊名称：Journal of Mathematical Finance
印刷版ISSN：2162-2434
电子版ISSN：2162-2442
出版年度：2016
卷号：06
期号：05
页码：930-943
DOI：10.4236/jmf.2016.65062
语种：English
出版社：Scientific Research Publishing
摘要：We study the free boundary problem of the American type of options. We consider a continuous dividend paying put option and provide a much simpler way of approximating the option payoff 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 define 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 fitting for option values. We consider stochasticity (an Ito process) as we define this transformation and this yields better approximations for option values and payoffs. We also numerically compute optimal option prices by using the same transformation. We finally demonstrate that our transformation performs better than most semi-analytic results.
关键词：Option Pricing;American Put Option;Free Boundary;Payoff;Stochastic Interpolation