A Numerical Analysis of Comparing Several Practical Approaches for Pricing both American and European Put Options

Abstract

Numerical methods are essential in option pricing
for handling complex derivatives, multi-asset scenarios, and
American options, where analytical solutions are impractical.
They offer flexibility, accuracy, and the ability to model realworld market conditions. The present paper compares numerical
pricing methods for European and American put option that
have yet to be studied. This study implements five basic
computational methods. Computer Algebra System (CAS)
Python is utilized for the simulations. For both European and
American put options, a tabular and graphical analysis of
various strategies is offered. The findings show that the CrankNicolson Finite Difference Method (CNFDM) yields better results
than the other approaches.