Comparison between VG-levy and Kernel function estimation with application

In this article, we present the variance Gamma Levy model that was obtained from the Brownian motion Gamma with their parameter estimation methods (Maximum Likelihood (MLE) and method of moments (MME)). Then, we compare them with Kernel density function depending on MASE. Our application concerned with the Apple company that is listed on the Nasdaq, their data are suitable for the VG-Levy model and achieved the proper conditions of Levy of stability and independence, which means that Apple company was efficient in providing the information to investors. The aim of studying the price fluctuations through the parameters of the model and thus the possibility of knowing the trends of stock prices in the financial markets and the consequent risks associated with investing in them in a manner consistent with the investor's preferences regarding bearing a certain degree of risk in the sense of a pre-preparedness for the potential sacrifice of the investor's capital with the limits of risk resulting from those fluctuations in prices for the returns resulting from price movements in those markets., So it was found that the VG-levy model with MLE is the best