A closed-form exact solution for the value of American put and its optimal exercise boundary

Song-Ping Zhu

doi:10.1117/12.609078

23 May 2005 A closed-form exact solution for the value of American put and its optimal exercise boundary (Invited Paper)

Song-Ping Zhu

Author Affiliations +

Proceedings Volume 5848, Noise and Fluctuations in Econophysics and Finance; (2005) https://doi.org/10.1117/12.609078
Event: SPIE Third International Symposium on Fluctuations and Noise, 2005, Austin, Texas, United States

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.

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Song-Ping Zhu "A closed-form exact solution for the value of American put and its optimal exercise boundary (Invited Paper)", Proc. SPIE 5848, Noise and Fluctuations in Econophysics and Finance, (23 May 2005); https://doi.org/10.1117/12.609078

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