Modeling Financial Assets with Geometric and Fractional Brownian Motion

Abstract

This paper analyzes the suitability of geometric Brownian motion, fractional Brownian motion, and geometric fractional Brownian motion for modeling stock price dynamics. Model parameters, including drift, volatility, and the Hurst exponent, are estimated using a designated training period for each asset. The accuracy of the model is then evaluated on testing-period data using the Kolmogorov–Smirnov test applied to standardized increments, which are expected to follow a standard normal distribution under the fitted models.