A Numerical Approximation on Black-Scholes Equation of Option Pricing

Abstract

This paper considered the notion of European option which is geared towards solving analytical and numerical solutions. In particular, we examined the Black-Scholes closed form solution and modified Black-Scholes (MBS) partial differential equation using Crank-Nicolson finite difference method. These partial differential equations were approximated to obtain Call and Put option prices. The explicit price of both options is found accordingly. The numerical solutions were compared to the closed form prices of Black-Scholes formula. More so, comparisons of other parameters were discussed for the purpose of investment plans. The computational results shows: increase in stock volatility increases the value of options, when the initial stock price is equal to its strike price the values of call option is higher than the put option. This informs the investor about the behavior of stock prices for the purpose of decision making.  Finally, all simulation results presented graphically using MATLAB.