  Six gravitational wave detections have been reported so far, providing
crucial insights on the merger rate of double compact objects. We investigate
the cosmic merger rate of double neutron stars (DNSs), neutron star-black hole
binaries (NSBHs) and black hole binaries (BHBs) by means of
population-synthesis simulations coupled with the Illustris cosmological
simulation. We have performed six different simulations, considering different
assumptions for the efficiency of common envelope (CE) ejection and exploring
two distributions for the supernova (SN) kicks. The current BHB merger rate
derived from our simulations spans from $\sim{}150$ to $\sim{}240$ Gpc$^{-3}$
yr$^{-1}$ and is only mildly dependent on CE efficiency. In contrast, the
current merger rates of DNSs (ranging from $\sim{}20$ to $\sim{}600$ Gpc$^{-3}$
yr$^{-1}$) and NSBHs (ranging from $\sim{}10$ to $\sim{}100$ Gpc$^{-3}$
yr$^{-1}$) strongly depend on the assumptions on CE and natal kicks. The merger
rate of DNSs is consistent with the one inferred from the detection of GW170817
only if a high efficiency of CE ejection and low SN kicks (drawn from a
Maxwellian distribution with one dimensional root mean square $\sigma{}=15$ km
s$^{-1}$) are assumed.
