The mismatch negativity (MMN) is an event related potential evoked by violations of regularity. Here, we present a model of the underlying neuronal dynamics based upon the idea that auditory cortex continuously updates a generative model to predict its sensory inputs. The MMN is then modelled as the superposition of the electric fields evoked by neuronal activity reporting prediction errors. The process by which auditory cortex generates predictions and resolves prediction errors was simulated using generalised (Bayesian) filtering--a biologically plausible scheme for probabilistic inference on the hidden states of hierarchical dynamical models. The resulting scheme generates realistic MMN waveforms, explains the qualitative effects of deviant probability and magnitude on the MMN - in terms of latency and amplitude--and makes quantitative predictions about the interactions between deviant probability and magnitude. This work advances a formal understanding of the MMN and--more generally--illustrates the potential for developing computationally informed dynamic causal models of empirical electromagnetic responses.