Applications in Finance: American Put Options

  • Shijun Liao

Abstract

The homotopy analysis method (HAM) is successfully combined with the Laplace transform to solve the famous American put option equation in finance. Unlike asymptotic and/or perturbation formulas that are often valid only a couple of days or weeks prior to expiry, our homotopy approximation of the optimal exercise boundary B(ι) in polynomials of \(\sqrt \tau \) to oM) may be valid a couple of dozen years, or even a half century, as long as M is large enough. It is found that the homotopyapproximation of B(ι) in polynomial of \(\sqrt \tau \) to o48) is often valid in so many years that the well-known theoretical perpetual optimal exercise price is accurate enough thereafter, so that the combination of them can be regarded as an analytic formula valid in the whole time interval 0≤ι<+∞. A practical Mathematica code APOh is provided in the Appendix 13.2 for businessmen to gain accurate enough optimal exercise price of American put option at large expiration-time by a laptop only in a few seconds, which is free available (Accessed 25 Nov 2011, will be updated in the future) at http://numericaltank.sjtu.edu.cn/HAM.htm

Keywords

Homotopy Analysis Method Exercise Price Optimal Exercise Convertible Bond Perturbation Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Shijun Liao
    • 1
  1. 1.Shanghai Jiao Tong UniversityShanghaiChina

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