  By means of a model Hamiltonian approach we study the role of volume
expansion, Hund's coupling and electron correlation in the standard
hybridization mechanism for ferroelectricity in cubic CaMnO$_3$, a prototypical
non-$d^0$ perovskite. Our results establish that the ferroelectric instability
arises from a subtle balance between different energy contributions, explaining
the origin of its enhancement under negative pressure. Expansion of volume is
found to cause a strong reduction of the elastic energy, while leaving almost
unchanged the tendency of Mn states to form covalent bonds with the surrounding
oxygens. Hund's coupling with local spins of magnetic cations can reduce and
even suppress the instability towards the ferroelectric state.
