In this talk I will present a mean-field model of `systemic risk' in large financial markets, seeking to capture simple notions of herding, common exposures, and default contagion. The mean-field limit (modelling the macroscopic health of the financial system) is described by a nonlinear SPDE on the positive half-line, which is the stochastic Fokker–Planck equation for an absorbing (conditional) McKean–Vlasov type SDE with common noise. During the talk, I will present results on the well-posedness along with some numerical illustrations. Moreover, I will consider a more singular variant of the mean-field limit, which can exhibit jump discontinuities coming from macroscopic cascades of contagion. In this latter case, I will present some results on how the occurrence of these discontinuities depend on the common noise. The talk is based on joint works with Ben Hambly and Sean Ledger.