Adaptive finite difference methods for valuing American options |
Posted on:2008-04-20 | Degree:M.Sc | Type:Thesis |
University:University of Toronto (Canada) | Candidate:Dang, Duy Minh | Full Text:PDF |
GTID:2440390005478244 | Subject:Computer Science |
Abstract/Summary: | |
We develop space-time adaptive methods for valuing American options with strong emphasis on American put options. We examine the application of adaptive techniques to the Black-Scholes partial differential equation problem associated with an American put option in the context of non-uniform second-order finite differences. At certain timesteps, we obtain a redistribution of the spatial points based on a monitor function that attempts to equidistribute the error. The proposed finite difference discretization on non-uniform grids and redistribution of the spatial points lead to linear complementarity problems with M-matrices. The Projected Successive Over-relaxation and a penalty method are considered to handle the free boundaries. We study and compare the accuracy and efficiency of the considered methods. A complete proof of convergence and uniqueness of the projected SOR method under certain conditions is also presented. |
Keywords/Search Tags: | Methods, American, Adaptive, Finite |
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