  This paper deals with an extension of the so-called Black-Scholes model in
which the volatility is modeled by a linear combination of the components of
the solution of a differential equation driven by a fractional Brownian motion
of Hurst parameter greater than $1/4$. In order to ensure the positiveness of
the volatility, the coefficients of that equation satisfy a viability
condition. The absence of arbitrages, the completeness of the market and a
pricing formula are established.
