We introduce a new model of financial market with stochastic volatility driven by an arbitrary Hölder continuous Gaussian Volterra process. The distinguishing feature of the model is the form of the volatility equation, which ensures that the solution is “sandwiched” between two arbitrary Hölder continuous functions chosen in advance. We discuss the structure of local martingale measures on this market, investigate integrability and Malliavin differentiability of prices and volatilities, and study absolute continuity of the corresponding probability laws. Additionally, we utilize Malliavin calculus to develop an algorithm of pricing options with discontinuous payoffs.