Bias-Corrected Method of Moments Estimation of the Hurst Parameter for Improved Option Pricing Under the Fractional Black-Scholes Model
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.026 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".