Determination of values of stocks and indices is very challenging and a very important aspect in finance. Knowing the value of a stock price, for instance, can be very vital in pricing various financial derivatives such as options. On the other hand, indices are useful tools for tracking stock market trends. By studying the pattern of index values over time, investors might gain insight that would help them make better investment decisions. Various attempts have been made to predict future stock prices and index values but these have yielded mixed results due to the stochastic nature of financial markets. Despite the fact that there has been growing academic interest in the stock market, it still remains elusive as to what the next day’s price of a stock, in particular, and value of an index, in general, will be even when the prices of the present and previous days are known. One of the popular approaches of pricing options, for instance, has been through the use of the Black-Scholes model. This and various other approaches have placed normality at the centre of the stochastic modeling. In this thesis, a statistical analysis on different indices and stocks traded on the world’s major financial markets is performed and demonstrates, through simulation, that Markov chains and the double gamma distribution play a central role in the stochastic behaviour of prices on the stock market.