2024/09/11 by Daniele Angelini, Matthieu Garcin, Angelini, Daniele +1
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Statistical Finance (q-fin.ST) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2409.07159
openalex publication_date 2024/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Ht, driven by a fractional Ornstein-Uhlenbeck (fOU) process. When the regularity parameter Ht is equal to 1/2, the efficient market hypothesis holds, but when Ht≠ 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 Ht of the FSRM, giving some insight into one's ability to forecast future price increments and to build statistical arbitrages with this model.