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We propose a dynamic mean field model for `systemic risk' in large financialsystems, which we derive from a system of interacting diffusions on thepositive half-line with an absorbing boundary at the origin. These diffusionsrepresent the distances-to-default of financial institutions and absorption atzero corresponds to default. As a way of modelling correlated exposures andherd behaviour, we consider a common source of noise and a form ofmean-reversion in the drift. Moreover, we introduce an endogenous contagionmechanism whereby the default of one institution can cause a drop in thedistances-to-default of the other institutions. In this way, we aim to capturekey `system-wide' effects on risk. The resulting mean field limit ischaracterized uniquely by a nonlinear SPDE on the half-line with a Dirichletboundary condition. The density of this SPDE gives the conditional law of anon-standard `conditional' McKean--Vlasov diffusion, for which we provide anovel upper Dirichlet heat kernel type estimate that is essential to theproofs. Depending on the realizations of the common noise and the rate of meanreversion, the SPDE can exhibit rapid accelerations in the loss of mass at theboundary. In other words, the contagion mechanism can give rise to periods ofsignificant systemic default clustering.

An SPDE Model for Systemic Risk with Endogenous Contagion