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We present a framework dedicated to modelling the resistive switching operation of Valence Change Memory (VCM) cells. The method combines an atomistic description of the device structure, a Kinetic Monte Carlo (KMC) model for the creation and diffusion of oxygen vacancies in the central oxide under an external field, and an ab-initio quantum transport method to calculate electrical current and conductance. As such, it reproduces a realistically stochastic device operation and its impact on the resulting conductance. We demonstrate this framework by simulating a switching cycle for a TiN/HfO$_2$/TiN VCM cell, and see a clear current hysteresis between high/low resistance states, with a conductance ratio of one order of magnitude. Additionally, we observe that the changes in conductance originate from the creation and recombination of vacancies near the active electrode, effectively modulating a tunnelling gap for the current. This framework can be used to further investigate the mechanisms behind resistive switching at an atomistic scale and optimize VCM material stacks and geometries.