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Proceedings Paper

A closed-form exact solution for the value of American put and its optimal exercise boundary
Author(s): Song-Ping Zhu
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Paper Abstract

Searching for a closed-form exact solution for American put options under the Black-Scholes framework has been a long standing problem in the past; many researchers believe that it is impossible to find such a solution. In this paper, a closed-form exact solution, in the form of a Taylor's series expansion, of the well-known Black-Scholes equation is presented for the first time. As a result of this analytic solution, the optimal exercise boundary, which is the main difficulty of the problem, is found as an explicit function of the risk-free interest rate, the volatility and the time to expiration.

Paper Details

Date Published: 23 May 2005
PDF: 14 pages
Proc. SPIE 5848, Noise and Fluctuations in Econophysics and Finance, (23 May 2005); doi: 10.1117/12.609078
Show Author Affiliations
Song-Ping Zhu, Univ. of Wollongong (Australia)

Published in SPIE Proceedings Vol. 5848:
Noise and Fluctuations in Econophysics and Finance
Derek Abbott; Jean-Philippe Bouchaud; Xavier Gabaix; Joseph L. McCauley, Editor(s)

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