Bias-Corrected Method of Moments Estimation of the Hurst Parameter for Improved Option Pricing Under the Fractional Black-Scholes Model

The Hurst parameter H plays a critical role in modeling long-memory behavior in financial time series, particularly within the framework of the fractional Black–Scholes model (fBSM). While the Method of Moments (MOM) provides a fast, closed-form estimator for H, it suffers from increasing negative bias, especially as H grows beyond 0.6. This paper proposes a bias-corrected version of the MOM estimator based on a quadratic regression fit derived from simulation data. The corrected estimator substantially reduces estimation error while retaining computational efficiency. Through extensive simulations, we quantify the impact of MOM bias on option pricing and demonstrate how our correction method leads to more accurate pricing under the fBSM. We apply the methodology to real financial assets—including Natural Gas, Apple, Gold, and Crude Oil—and show that the corrected Hurst estimates reduce option pricing error by up to USD 0.47 per contract relative to the uncorrected estimator, depending on the asset’s volatility structure. These results underscore the importance of accurate Hurst parameter estimation for derivative pricing, particularly in volatile markets such as energy and commodities, while also remaining relevant to equities and precious metals. The corrected estimator thus offers practitioners a simple yet effective tool to improve financial decision-making.