A Front Fixing Crank-Nicolson Finite-Difference for the Solvability of the American Put Option Models

Abstract

In this paper, a new approach to solve the American put option pricing model has been discussed. The method is based on the front-fixing Crank-Nicolson finite-difference method with the reliance on the Caputo-Fabrizio stochastic fractional derivative with regular kernel. The American put option pricing model is one of the most important models used in finance to determine the value of an option that gives the holder the right to sell an underlying asset at a given price. The approach in this paper deals with early exercise through the use of front-fixing technique that makes it easier and more effective to compute values of American put options. To this end, the method presented here is shown to be stable, precisely effective, and efficient as compared to the existing methods in the literature. Numerical experiments performed also confirm the efficiency of the suggested method and its capability to provide reliable and accurate prices of American put options using a stable scheme.