Different molecular simulation strategies are used to assess the stability of methane hydrate under various temperature and pressure conditions. First, using two water molecular models, free energy calculations consisting of the Einstein molecule approach in combination with semigrand Monte Carlo simulations are used to determine the pressure- temperature phase diagram of methane hydrate. With these calculations, we also estimate the chemical potentials of water and methane and methane occupancy at coexistence. Second, we also consider two other advanced molecular :simulation techniques that allow probing the phase diagram of methane hydrate: the direct coexistence method in the Grand Canonical ensemble and the hyperparallel tempering Monte Carlo method. These two direct technique's are found to provide stability conditions that are,consistent with the pressure temperature phase diagram obtained using rigorous free energy calculations: The phase diagram obtained in this work, which is found to be consistent with previous simulation studies, is close to its experimental counterpart provided the TIP4P/Ice model is used to describe the water molecule.