Benoît Mandelbrot, the father of Fractal Geometry, developed a multifractal model for describing price changes. Despite the commonly used models, such as the Brownian motion, the Mutifractal Model of Asset Return (MMAR) takes into account scale-consistency, long-range dependence and heavy...

This paper proposes the generalized use of fractional Brownian motion in a multifractal trading time framework to reveal variation in the index price diffusion process that appears before and after 'extreme' events of distinct origin. "Crashes" following internal self-organization and those...

The Multifractal Embedded Branching Process (MEBP) process and Canonical Embedded Branching Process (CEBP) process were introduced by Decrouez and Jones (2012). The CEBP is a process in which the crossings of dyadic intervals constitute a branching process. An MEBP process is defined as a...

We develop a financial market model using an Ising spin system on a Sierpinski carpet lattice that breaks the equal status of each spin. To study the fluctuation behavior of the financial model, we present numerical research based on Monte Carlo simulation in conjunction with the statistical...