Black scholes option pricing model - brownian motion approach

Brownian motion has become one of the fundamental building blocks of modern quantitative finance. The mathematical theory of Brownian motion has been applied in contexts ranging far beyond the movement of particles in fluids. Until recently, stock market researchers have confronted the same problem. While they can chart the path of the market on a minute by minute basis it is very hard for them to observe who buys, who sells and how demand and supply affects price fluctuations. There exist many researchers about how the behavior of different investors makes the option price movement in a stock market. The purpose of this paper is to construct the Black Scholes option pricing model in the stock markets by using Brownian motion approach. The main ambition of this study is fourfold: 1) First we begin our approach to construction of Brownian motion from the simple symmetric random walk. 2) Next we introduce the Black – Scholes option pricing model with stock price movement by using of Geometric Brownian motion. 3) Then we extent this Brownian motion approach in the stock market and 4) Finally we construct the model for the generalization based on the deformation of the standard Brownian motion and Black Scholes pricing formula. And this paper will end with conclusion.