We present a method that takes advantage of the Brownian motion of a colloidal particle to experimentally determine the area stretch modulus of giant liposomes in solution, in regard to the continuum mechanics theory of elasticity. The characteristic parameters of the corresponding model are measured by using the three-dimensional version of digital video microscopy. Such an approach makes use of the diffraction pattern generated by fluorescent spheres found below the focal plane of the microscope objective, allowing the spatial location of the sphere and, thus, the reconstruction of its trajectory. When this particle probe is localized in the neighborhood of a bilayer membrane, its motion causes an elastic distortion of the membrane that is quantifiable. More importantly, such deformation is related to the mentioned modulus, whose measured values are consistent with experimental data obtained through well-known techniques.