Modelling of Market Stock Using the Normal Variance Models

Abstract

Great work has been done on modeling of nancial instruments namely,shares,equities, stocks and many more.The focus of this thesis is mainly modeling of stocks based on normal mixtures.The essence of this work is to do a comparison between the Normal Variance Mean Model and Normal Variance model and determine which of the two is best for modeling stocks. Normal mixtures is a combination of two distributions where the normal distribution is the conditional distribution and is mixed with another distribution as the mixing distribution. The two mixing distribution discussed in this thesis are both Gamma and Inverse Gaussian distributions ,out of which we get the Variance Gamma and Normal Inverse Gaussian distributions respectively.Data is tted on the distributions, Normal variance model and the Normal Variance Mean Model and a comparison is done to ascertain which model gives the best goodness of t and is the best model. Construction of the two distributions based on Normal Variance is done using two approaches that is; Saralees Nadarajah and Ole Barndo , and their respective properties are given. Their respective Maximum likelihood Estimators based on the two distributions is also determined. Estimation of the two models is e ected using Method of Moments. Data from Standard and Poor’s 500 index,January 1977- December has been used for the analysis of the given work,and the results have been discussed accordingly. With regard to AIC test done in the analysis Skewed Variance Gamma distribution gives the best goodness of t as compared to the other distributions While Nadarajah’s Approach Normal Inverse Gaussian distribution tends to be the model for tting stock returns