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 )



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