The GARCH Model Driven by Fractional Brownian Motion

ABSTRACT This article presents a novel extension of the GARCH model incorporating weighted liquidity, modeled by fractional Brownian motion. The existence of a stationary solution is proven, and the higher‐order moments are calculated to illustrate the statistical properties of the model. Analysis of the auto‐correlation function of the squared process confirms the long‐term memory characteristic of the model. Numerical simulations are employed to validate the theoretical findings, demonstrating the significance of the model in the financial market.