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 .