**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

* *Copyright statement for the code **APO**

Mathematica
Package **APOh** for businessman

Code **APOh **for
Mathematica 5.2 Code **APOh** for Mathematica 8.0

Copyright statement for the code **APOh**

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**