Every geodesic loop on a closed hyperbolic surface lifts canonically to the unit tangent bundle and its complement is a three-manifold. Foulon and Hasselblatt showed that this three-manifold is hyperbolic if the geodesic loop is filling. In this talk we will study the hyperbolic volume of such complements. More precisely, we will see that for a ?generic" filling geodesic there is a lower bound for the volume of its complement in terms of its hyperbolic length. This is joint work with Tommaso Cremaschi, Didac Martinez-Granado and Franco Vargas Pallete.