Stochastic Analysis of Black –Scholes Model of Option Pricing for Economic Investments.

Abstract

This paper considered an option pricing model which could be used for decision making in stock trading business. In particular, we studied the Black-Scholes model of European option which gave closed form prices of Call and Put option prices with disparities of some statistical parameters affecting real life changes. The Quantiles-Quantiles (Q-Q) normality tests were considered on Call and Put options prices which showed that they are significantly correlated and normally distributed. We also conducted hypothesis testing via Kolmogorov Smirnov (KS) and result violated an assumption of Black-Scholes that stipulated that volatility is constant throughout the trading days and graphical result were used to authenticate the violation of Black-Scholes model of option pricing. The results obtained here has profound financial benefits for economic investments.