Simulation of multifractal products of Ornstein–Uhlenbeck type processes

This paper investigates and provides evidence of the multifractal properties of products of the exponential of Ornstein–Uhlenbeck processes driven by Lévy motion. We demonstrate in detail the construction of a multifractal process with gamma subordinator as the background driving Lévy process. Simulations are performed for the scenarios corresponding to the normal inverse Gaussian, gamma and inverse Gaussian distributions. The log periodograms and Rényi functions of the simulated processes are also computed to investigate their multifractality.