A Mean Convection Finite Difference Method for Solving Black Scholes Model for Option Pricing

TL;DR

This paper introduces a novel Mean Convection Finite Difference Method for European option pricing under the Black-Scholes model, demonstrating improved accuracy and efficiency over traditional methods through numerical experiments.

Contribution

The paper presents a new finite difference approach with a tuning parameter for convection, enhancing stability and accuracy in option pricing models.

Findings

The proposed method outperforms Crank-Nicolson and Monte Carlo in accuracy.

It demonstrates faster computation times.

The method maintains stability across various parameters.

Abstract

In this research, we proposed a Mean Convection Finite Difference Method (MCFDM) for European options pricing. The Black-Scholes model, which describes the dynamics of a financial asset, was first transformed into a convection-diffusion equation. We then used the finite difference method to discretize time and price, and introduced a tuning parameter to enhance the convection term. Specified the boundary and initial conditions for call and put options of European options, and performed numerical calculations to obtain a numerical solution and error estimation. By varying the strength of the strike price and risk-free interest rate, we explored the accuracy and stability of our predicted prices. Finally, we compared our proposed method with those obtained using the Crank-Nicolson Finite Difference Method (CFDM) and Monte Carlo method. Our numerical results demonstrate the efficiency and accuracy of our proposed method, which outperformed the CFDM and Monte Carlo methods in terms of accuracy and speed.