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
