  Let $\Phi:\R\rightarrow\R$ be an arbitrary continuously differentiable
deterministic function such that $|\Phi|+|\Phi'|$ is bounded by a polynomial.
In this article we consider the class of stochastic volatility models in which
${Z(t)}_{t\in [0,1]}$, the logarithm of the price process, is of the form
$Z(t)=\int_{0}^t \Phi(X(s)) dW(s)$, where ${X(s)}_{s\in[0,1]}$ denotes an
arbitrary centered Gaussian process whose trajectories are, with probability 1,
H\"older continuous functions of an arbitrary order $\alpha\in (1/2,1]$, and
where ${W(s)}_{s\in[0,1]}$ is a standard Brownian motion independent on
${X(s)}_{s\in [0,1]}$.
  First we show that the critical H\"older regularity of a typical trajectory
of ${Z(t)}_{t\in[0,1]}$ is equal to 1/2. Next we provide for such a trajectory
an expression as a random series which converges at a geometric rate in any
H\"older space of an arbitrary order $\gamma<1/2$; this expression is obtained
through the expansion of the random function $s\mapsto \Phi(X(s))$ on the Haar
basis. Finally, thanks to it, we give an efficient iterative simulation method
for ${Z(t)}_{t\in[0,1]}$.
