Brownian Motion and the Black-Scholes Option Pricing Formula

Abstract

The Brownian Motion of visible particles suspended in a fluid   led to one of the first accurate determination   of the mass   of the visible molecules.  Mathematical model of Brownian motion   has numerous real world applications. For instance stock market fluctuations.  The Black- Scholes  model  for calculating  the premium of  an option  was introduced  in 1973 in a paper   published in  Journal  of Political Economy  developed by three Economists –Fisher Black, Myron Scholes  and Robert Merton and  is world’s  most  well known  Option Pricing Model . In 1997 all was awarded    Nobel Prize in Economics.

Keywords: Brownian  Motion, Market fluctuations, Arbitrage Theorem, Random Walk, Hitting Time, Betting.