A comparison between analytic and numerical solution of linear Black-Scholes equation governing option pricing: Using BANKNIFTY

Black Scholes(B-S) model is one of the popular methods of calculating the option prices. It consists of the closed form solution of the linear Black Scholes equation. Researchers have also found the numerical solutions of the Black Scholes equation which is much more intuitive compared to its closed form solution. In this paper, we have compared the analytical solution with the numerical solution of linear Black-Scholes equation governing option pricing. Finite Difference methods (FDMs) are used to discretize B-S equation base on three different schemes namely, Explicit, Implicit and the Crank Nicholson scheme. We have also tried to found out whether this solution are validate to compute the price the options of the higher strike prices such as those of BANKNIFTY options. It is also showed that numerical solutions are independent of number of grids.