  The sub-fractional Brownian motion (sfBm) is a stochastic process,
characterized by non-stationarity in their increments and long-range
dependency, considered as an intermediate step between the standard Brownian
motion (Bm) and the fractional Brownian motion (fBm). The mixed process, a
linear combination between a Bm and an independent sfBm, called mixed
sub-fractional Brownian motion (msfBm), keeps the features of the sfBm adding
the semi-martingale property for H>3/4, is a suitable candidate to use in price
fluctuation modeling, in particular for option pricing. In this note, we arrive
at the European Call price under the Constant Elasticity of Variance (CEV)
model driven by a mixed sub-fractional Brownian motion. Empirical tests show
the capacity of the proposed model to capture the temporal structure of option
prices across different maturities.
