We investigate the local elastic properties of polystyrene doped with SiO2 nanoparticles by analyzing thelocal density fluctuations. The density fluctuations were established from coarse-grained molecular dynamics simulations performed with theMARTINI force field. A significant increase in polystyrene stiffness was revealed within a characteristic range of 1.4 nm from the nanoparticle, while polystyrene density saturates to the bulk value at significantly shorter distances. The enhancement of the local elastic properties of the polymer was attributed to the effect of nonaffine deformations at the length scale below 1 nm, which was further confirmed through the random matrix model with variable strength of disorder.