 A closed-form solution to American options under general diffusion processesJing Zhao and Hoi Ying Wong Quantitative Finance, 2012, vol. 12, issue 5, 725-737 Abstract: This paper investigates American option pricing under general diffusion processes. Specifically, the underlying asset price is assumed to follow a diffusion process in which both the dividend yield and volatility are functions of time and the underlying asset price. Using the generalized homotopy analysis method, the determination of the early exercise boundary is separated from the valuation procedure of American options. Then, an exact and explicit solution for American options on a dividend-paying stock is derived as a Maclaurin series. In addition, the corresponding optimal early exercise boundary and the Greeks are obtained in closed-form solutions. A nonlinear sequence transformation, the Pad� technique, is used to effectively accelerate the convergence of the partial sums of the infinite series. As the homotopy constructed in this paper is based on a generalized deformation with a shape parameter and kernel function, the error of the homotopic approximation could be reduced further for a fixed order. Numerical examples demonstrate the validity, effectiveness, and flexibility of the proposed approach. Date: 2012 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:quantf:v:12:y:2012:i:5:p:725-737 Ordering information: This journal article can be ordered from DOI: 10.1080/14697680903193405 Access Statistics for this article Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral More articles in Quantitative Finance from Taylor & Francis Journals |
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