  In this work we introduce an interbank network with stochastic dynamics
subject to an endogenous notion of distress contagion that accounts for worries
about future defaults within the network. Specifically, this entails a
forward-backward approach to the equilibrium dynamics, enforced by a
mark-to-market valuation adjustment for interbank claims, whereby the
conditional probabilities of future defaults are required to determine today's
balance sheets. Distinct from static models, the resulting distress contagion
acts as a stochastic volatility term which leads, endogenously, to volatility
clustering and a marked downside leverage effect. Moreover, by considering
multiple maturities, our model provides a systemic risk-aware term structure
for interbank claims. We present the analysis in two parts: (i) a single
maturity setting that closely matches the traditional interbank network
literature, and (ii) a multiple maturity setting to examine the impact of
systemic risk on the full term structure. Numerical case studies are presented
throughout to demonstrate the financial implications of this systemic risk
model.
