  A diffusion Monte Carlo simulation of superfluid $^4$He at zero temperature
and pressures up to 275 bar is presented. Increasing the pressure beyond
freezing ($\sim$ 25 bar), the liquid enters the overpressurized phase in a
metastable state. In this regime, we report results of the equation of state
and the pressure dependence of the static structure factor, the condensate
fraction, and the excited-state energy corresponding to the roton. Along this
large pressure range, both the condensate fraction and the roton energy
decrease but do not become zero. The roton energies obtained are compared with
recent experimental data in the overpressurized regime.
