Abstract :Jameel’s Criterion and Jameel’s Advanced Stressed Models (2015) were introduced to capture Low-Probability, High-Impact Events in the existing Default and Derivatives Pricing Models. “Stock Prices are perhaps the most closely watched Economic variables to date”. The existing models (Simple and Fractional Brownian Motion as well as Stable Distributions) have difficulties in identifying the right tail distribution (process), that is whether to use power-type or exponential-type distributions; the stable distributions generalize normal distribution; Geometric Brownian Motion (GBM) can only be used to forecast maximum of two weeks closing prices and does not include cyclical or seasonal effects together with the periods of constant values according to (Kou (2002); Abidin and Jaffar (2014); Marathe and Ryan (2005); Gajda and Wylomanka (2012)) respectively.