A fractal-based approach for modeling stock price variations

Abstract

The recent global financial crisis has threatened the financial system with total collapse of many economic sectors with a particular penetration to world's stock markets. The large swings in the prices of international stocks or indexes have reinvigorated the debate on their mathematical modeling. The traditional approaches do not seem to be very exhaustive and satisfactory, especially when extreme events occur. We propose a fractal-based approach to model the actual prices by assuming that they follow a Multifractional Process with Random Exponent. An empirical evidence is offered that this stochastic process is able to provide an appropriate modeling of actual series in terms of goodness of fit by comparing three main stock indexes.