Contagion-based safety premium in bank networks

We examine safety premiums through the lens of financial contagion in interbank networks. In our model with endogenous collateralized lending contracts, safe assets command premiums because they relax funding constraints without amplifying default propagation. Multiple equilibria characterized by distinct lending volumes and safety premiums emerge exclusively in networks containing directed cycles. The safety premium thus serves as a tractable, price-based statistic of systemic fragility. Comparative statics show that conditions weakening contagion—most notably a sufficiently high safe-to-risky-asset ratio—can eliminate equilibrium multiplicity. Pure-strategy high-lending equilibria survive only when collateral quality is sufficiently high. Network structure critically influences these dynamics: increased density introduces competing effects (amplified contagion risk versus enhanced liquidity coinsurance), with their relative dominance determined by loan sizes and collateral quality. Core-periphery networks generate higher safety premiums than complete networks, as peripheral banks respond defensively to the amplified contagion risk circulating within the core. A greater number or larger size of peripheral banks leads to a higher safety premium.