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
Mathematica Package APOh for businessman
( They are obtained by using the Mathematica code APO )