  We introduce a heterogeneous formulation of a contagious McKean-Vlasov
system, whose inherent heterogeneity comes from asymmetric interactions with a
natural and highly tractable structure. It is shown that this formulation
characterises the limit points of a finite particle system, deriving from a
balance sheet based model of solvency contagion in interbank markets, where
banks have heterogeneous exposure to and impact on the distress within the
system. We also provide a simple result on global uniqueness for the full
problem with common noise under a smallness condition on the strength of
interactions, and we show that, in the problem without common noise, there is a
unique differentiable solution up to an explosion time. Finally, we discuss an
intuitive and consistent way of specifying how the system should jump to
resolve an instability when the contagious pressures become too large. This is
known to happen even in the homogeneous version of the problem, where jumps are
specified by a 'physical' notion of solution, but no such notion currently
exists for a heterogeneous formulation of the system.
