A Front Fixing Crank-Nicolson Finite Deference for the American Put Options Model

TL;DR

This paper introduces a novel front-fixing Crank-Nicolson finite difference method for efficiently and accurately pricing American put options, addressing early exercise features with stability and positivity guarantees.

Contribution

It presents a new front-fixing technique combined with Crank-Nicolson scheme for American put options, improving stability, accuracy, and efficiency over existing methods.

Findings

Method is stable, accurate, and efficient.

Numerical results demonstrate effective pricing of American put options.

Positivity and monotonicity of coefficients are maintained under certain conditions.

Abstract

In this paper, we present a novel approach to solving the American put options pricing model by hugely relying on a front-fixing Crank-Nicolson finite difference method. Since the American put option pricing model is a widely used financial model for valuing an option with the right to sell an underlying asset at a fated price which generally decided in advance. The method we proposed here, solves the problem of early exercise by introducing a front-fixing technique that permits for efficient and accurate valuation of an American put option. As in the comparison to other approaches in the existing literature, we can assert that this method is stable, accurate, consistent, and efficient. The results that we obtained here from the numerical experiments demonstrate not only the efficacy of the proposed method but also in consistently and accurately pricing American put options with a stable scheme. Under some appropriate conditions on the step size discretization, we also show the positivity and monotonicity of the coefficient involved in the numerical scheme used.