Mathematica codes for American put option

American put option is governed by a partial differential equation (PDE) with an unknown moving boundary (i.e. the optimal exercise boundary). The homotopy analysis method (HAM) is successfully applied to solve this famous problem in finance. Unlike asymptotic and/or perturbation formulas that are often valid only a couple of days or weeks prior to expiry, the optimal exercise boundary given by the HAM may be valid a couple of dozen years, or even a half century! This illustrates the great potential and general validity of the HAM for nonlinear PDE. A practical Mathematica code APOh with a simple user’s guide is provided 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.

For details, please refer to Shijun Liao’s book: Homotopy Analysis Method in Nonlinear Differential Equations

Mathematica code APO for American put option

Code APO for Mathematica 5.2 Code APO for Mathematica 8.0

Mathematica Package APOh for businessman

Code APOh for Mathematica 5.2 Code APOh for Mathematica 8.0

A simple users guide of the code APOh

Data-files for Mathematica Package APOh: APO-48-10.txt APO-24-10.txt

( They are obtained by using the Mathematica code APO )

HAM: Introduction Basic Ideas & Brief History Publications Examples Mathematica Package BVPh