Numerical Analysis Of Black–Scholes Equation Using Crank-Nicolson Finite Difference Method

Abstract

This work uses the Crank-Nicolson finite difference method to analyze the numerical solution of the Black-Scholes equation. The Black–Scholes equation, as used in mathematical finance, is a partial differential equa tion (PDE) that governs how much a European call or European put will change in value over time. Several researchers have attempted to use various analytical and numerical methods to determine the solu tion of this Black-Scholes partial differential equation. The numerical solution of the Black-Scholes equation using the Crank-Nicolson finite difference approach, however, has not received considerable attention in the literature. The results demonstrate that the option value first stays zero for specific stock price values and then rises in line with the increase in stock price. As the operation time grows, the option value in the Black-Scholes equation progressively increases. It also shows that the option value in the Black-Scholes equation increases in conjunction with an increase in the interest rate and decreases in parallel with an increase in the underlying exercise price. The obtained findings gen erally demonstrate the effectiveness of the finite difference method in inding the numerical solutions to the Black-Scholes equation