My thesis tittled, "STOCK EXCHANGE MARKET PRICES AND THEIR EMPIRICAL ANALYSIS USING THE BLACK SCHOLES AND GARCH MODELS" , basically aims at investigating the two major critics of the Black Scholes Model that is, its assumption that the returns of the underlying assets in a financial market are normally distributed and that the volatility during this time is assumed to be constant. This was achieved by using NASDAQ Composite Index 2014-2018 dataset where this model was also compared with one of the most accurate GARCH Models between GARCH(1,1), EGARCH(1,1), IGARCH(1,1) and FIGARCH(1,0,1). Statistical tools such as Root Mean Squared and Information Criterions (Bayesian and Akaike) were employed to determine the accuracy. The study also recommends according to the findings on whether and why either Black Scholes Model and one of the GARCH Models is better than the other in volatility forecasting.