Massive black holes are located in the centre of all massive galaxies. During the encounter of galaxies those black holes pair and, after some hardening period, become sources of gravitational waves (GWs).  Binaries at the early stage of inspiral emit almost monochromatic GWs and the population of massive black hole binaries (MBHBs) is the main source for the Pulsar Timing Array (PTA).  In PTA we use radio emission from the millisecond pulsars to detect GWs in the nano-Hz frequency band. MBHBs will eventually merge releasing an immense amount of energy in GWs in the milli-Hz band where the future space-based GW observatory LISA will operate.  The main objective of this project is to use a population of MBHBs to study GW signal across all low frequencies: from nano-Hz with PTA to milli-Hz with LISA. This project is a part of french collaboration between several laboratories aiming at simulating the population of MBHBs and studying its properties in GWs and in the electromagnetic spectrum. Observation of GWs from merging MBHBs will be used to infer cosmological parameters and constrain the rate of expansion of the Universe.