[AaronBrown]

Fractional brownian motion is almost impossible to work with empirically. That is, you can specify a model and solve it, but it's not practical to look at real data and fit it back to a model. Tiny, high frequency variations will dominate your estimation. For one specific example, the periodic blind posting and position changes would defeat your fitting.

A much more robust model is to assume the drift rate follows a random walk. Even this is not easy to fit with any reasonable amount of data, but at least it tends to calibrate to the large swings, which is what you want to explain, rather than microstructure.