Market information of the fractional stochastic regularity model

TL;DR

This paper introduces the Fractional Stochastic Regularity Model (FSRM), extending Black-Scholes to account for multifractal price dynamics using a multifractional process with a random Hurst exponent, and analyzes its informational properties.

Contribution

It provides a theoretical analysis of the FSRM's regularity process using information theory, offering insights into price predictability and arbitrage opportunities.

Findings

The Hurst exponent $H_t$ indicates market efficiency when equal to 1/2.

Deviations of $H_t$ from 1/2 reveal potential for trend prediction.

The serial information of $H_t$ can be quantified using Shannon's entropy.

Abstract

The Fractional Stochastic Regularity Model (FSRM) is an extension of Black-Scholes model describing the multifractal nature of prices. It is based on a multifractional process with a random Hurst exponent $H_t$, driven by a fractional Ornstein-Uhlenbeck (fOU) process. When the regularity parameter $H_t$ is equal to $1/2$, the efficient market hypothesis holds, but when $H_t\neq 1/2$ past price returns contain some information on a future trend or mean-reversion of the log-price process. In this paper, we investigate some properties of the fOU process and, thanks to information theory and Shannon's entropy, we determine theoretically the serial information of the regularity process $H_t$ of the FSRM, giving some insight into one's ability to forecast future price increments and to build statistical arbitrages with this model.