Analysis of fractional Black-Scholes, Ornstein-Uhlenbeck, and Langevin models: a minimum distance estimation approach

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Hassane Goudja Izaddine
Siradhi Deme
Ali Souleyman Dabye

Abstract

The present research investigates parameter estimation in fractional stochastic models, specifically the Fractional Black-Scholes, Fractional Ornstein-Uhlenbeck, and Fractional Langevin models. These models, driven by fractional Brownian motion (fBm), capture long-memory effects and complex dependencies often observed in financial and physical systems. To efficiently estimate the parameters of these models, we apply the Minimum Distance Estimation (MDE) method. This approach tackles the challenges posed by long-range dependence, ensuring both asymptotic consistency and normality. We analyze the asymptotic properties of the estimators, including their consistency, asymptotic normality, and efficiency. By providing a unified theoretical framework, the current research highlights the robustness and applicability of the MDE method for parameter inference in fractional models. The findings contribute significantly to diverse fields such as quantitative finance, econometrics, and statistical physics.

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How to Cite
Izaddine, H. G., Deme, S., & Dabye, A. S. (2025). Analysis of fractional Black-Scholes, Ornstein-Uhlenbeck, and Langevin models: a minimum distance estimation approach. Gulf Journal of Mathematics, 19(1), 217-250. https://doi.org/10.56947/gjom.v19i1.2545
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