I feel that the dynamic of financial market is not really modeled by standard Brownian motion, but fractional Brownian motion or even multifractional Brownian motion.
I have read some references on Hurst exponent of stock prices and I get a feeling that the Hurst exponent may be random, too, since:
It should be mean-reversion
It has fluctuation around crisis.
May I ask what else empirical properties Hurst exponent should follow?
Are there any reference on modeling it?
Thank you so much!