  The Generalized fractional Brownian motion (gfBm) is a stochastic process
that acts as a generalization for both fractional, sub-fractional, and standard
Brownian motion. Here we study its use as the main driver for price
fluctuations, replacing the standard Brownian Brownian motion in the well-known
Black-Scholes model. By the derivation of the generalized fractional Ito's
lemma and the related effective Fokker-Planck equation, we discuss its
application to both the option pricing problem valuing European options, and
the computation of Value-at-Risk and Expected Shortfall. Moreover, the option
prices are computed for a CEV-type model driven by gfBm.
