<p>We consider stochastic volatility dynamics driven by a general Hölder-continuous Volterra-type noise and with unbounded drift. For these so-called SVV models, we consider the explicit computation of quadratic hedging strategies. While the theoretical hedge is well known in terms of the non-anticipating derivative for all square-integrable claims, the fact that these models are typically non-Markovian provides a challenge in the direct computation of conditional expectations at the core of the explicit hedging strategy. To overcome this difficulty, we propose a Markovian approximation of the model which stems from an adequate approximation of the kernel in the Volterra noise. We study the approximation of the volatility, of the prices and of the optimal mean-square hedge. We provide corresponding error estimates. The work is completed with numerical simulations.</p>