On Discontinuity and Persistence in the Returns on Financial Assets: New Simulation-Based Evidence Derived From a Multifractal Model of Asset Returns

Abstract

According to Mandelbrot, financial assets are characterized by two characteristic traits—discontinuity and price persistence. This paper uses simulations to obtain predictions for these two key features derived from a multifractal model of asset returns (MMAR). Following Mandelbrot, this paper uses the exponents of power laws to study asset return discontinuity, whereas the level of price persistence is measured via Hurst exponents. Using the distributions of these exponents derived from MMAR simulations, this study proposes a novel joint test designed to examine whether the MMAR is capable of describing the return data on financial assets with respect to these two key traits. Intriguingly, empirical tests suggest that the benchmark MMAR specification employed here is capable of describing discontinuity and persistence observed for the returns on five key financial asset markets—U.S. equities, USD/GBP exchange rates, gold futures, crude oil futures and Bitcoin. From a theoretical perspective, the findings are consistent with the possibility that common latent mechanisms, including herding behavior, may contribute to return dynamics across otherwise unrelated asset markets.