Type
Text
Type
Dissertation
Advisor
Li, Xiaolin , Rachev, Svetlozar | Xing, Haipeng | Holod, Dmytro.
Date
2011-08-01
Keywords
Applied mathematics | American option, FronTier, Front Track, Heston Model
Department
Department of Applied Mathematics and Statistics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/71524
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
This thesis is concerned with the numerical solution of the American option valuation problem formulated as a free boundary/initial value model. While other studies have focused on modified pricing model, formulating the problem as a non-linear model, using the front-fix method to fix the moving boundary, or trying to find semi-/analytical solutions to the problem, we introduce and analyze a front-tracking (FT) finite difference method (FDM) based on original Black-Scholes Model. The basis of the B-S Model, FDM, FT and options theory will be introduced. The numerical experiments performed indicate that the front tracking method considered is an efficient alternative for approximating simultaneously the option value and optimal exercise boundary functions associated with the valuation problem. We also extend the study to pricing options with stochastic volatility using Heston Model, as well as valuation of multi-asset options. | 76 pages
Recommended Citation
Zhang, Fan, "Pricing European and American Options in FronTier Framework and Other Applications" (2011). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 729.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/729