Forecasting Price Behavior with Fractional Stochastic Regularity

Summary

The Fractional Stochastic Regularity Model extends the Black–Scholes framework to represent multifractal price behavior. It uses a multifractional process whose time-varying regularity, expressed through a random Hurst exponent, is driven by a fractional Ornstein–Uhlenbeck process. The paper studies properties of that driving process and asks whether the regularity parameter contains serial information relevant to future price changes.

The model associates a Hurst exponent of one half with the efficient market hypothesis; values away from one half imply that past returns may carry information about trend or mean-reversion in log prices. The authors use information theory and Shannon entropy to characterize this information theoretically, with possible implications for forecasting increments and constructing statistical arbitrage. The excerpt supplies no empirical results or trading performance, so it does not establish that the theoretical signal is observable or profitable in practice.

Key ideas

• The model extends Black–Scholes using multifractal price dynamics and a time-varying Hurst exponent.
• A fractional Ornstein–Uhlenbeck process drives changes in the regularity parameter.
• The model links a Hurst exponent of one half to the efficient market hypothesis.
• Departures from one half may imply trend or mean-reversion information in past returns.
• Shannon entropy is used to study serial information, but the excerpt gives no empirical profitability evidence.

Tags

# Market information of the fractional stochastic regularity model


# Market information of the fractional stochastic regularity model









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.

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