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On convergence of a semi-analytical method for American option pricing |
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| Authors: | Xiaotie Deng Yonggeng Gu Shunming Zhang |
| Affiliation: | a Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong, China b Department of Mathematics, Hunan Normal University, Changsha 410081, Hunan, PR China c Academy of Mathematics and Systems Science, The Chinese Academy of Sciences, Beijing 100080, PR China d Department of Economics, The University of Western Ontario, London, Ontario, Canada N6A 5C2 e School of Economics and Finance, Victoria University of Wellington, PO Box 600, Wellington, New Zealand |
| Abstract: | We examine the valuation of American put options by a semi-analytical method, and obtain the prior estimate and the convergence of the approximate solution. Our proofs are based on the embedding theorem in Sobolev space and the theory of functional analysis, in particular, the theory of weak compactness. The results in this paper theoretically confirm empirical observations that these methods are accurate and computationally efficient. |
| Keywords: | American option Free boundary Prior estimate Semi-analytic method Convergence |
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