Author(s)

Ronald Katende¹, Diaraf Seck², Philip Ngare³

¹Pan African University, Institute of Basic Science, Technology and Innovation, JKUAT, Nairobi, Kenya.
²Departement de Mathematiques de la Decision, Universite Cheikh Anta Diop, Dakar-Fann, Senegal.
³School of Mathematics, University of Nairobi, Nairobi, Kenya.

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.

Option Pricing, American Put Option, Free Boundary, Payoff, Stochastic Interpolation

Katende, R. , Seck, D. and Ngare, P. (2016) On the Location of a Free Boundary for American Options. Journal of Mathematical Finance, 6, 930-943. doi: 10.4236/jmf.2016.65062.