A mathematical model of random paths
Fractional Brownian motion is a stochastic process whose increments can exhibit dependence. A geometric transformation can be used to construct positive-valued simulated paths. It is a modelling device, not evidence that financial prices follow the model.
The Hurst parameter
The parameter H lies between 0 and 1. In the idealised process, H = 0.5 corresponds to Brownian motion; larger and smaller values imply different dependence properties. Estimating H from a short or changing dataset can be unreliable.
Simulations are conditional examples
Drift, volatility, dependence and numerical choices determine the generated paths. An average simulated path is a model output, not a validated price forecast. Apparent patterns in historical data may disappear, and fitting past data does not demonstrate predictive accuracy.
Scope of this explanation
This page uses no named-security forecast, trading signal or price target. It does not claim that GFBM outperforms other models. Validation would require an explicit dataset, time period, benchmark and out-of-sample error analysis.