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This paper studies existence and uniqueness of equilibrium prices in a modelof the banking sector in which banks trade contingent convertible bonds withstock price triggers among each other. This type of financial product wasproposed as an instrument for stabilizing the global banking system after thefinancial crisis. Yet it was recognized early on that these products may createcircularity problems in the definition of stock prices - even in the absence oftrade. We find that if conversion thresholds are such that bond holders areindifferent about marginal conversions, there exists a unique equilibriumirrespective of the network structure. When thresholds are lower, existence ofequilibrium breaks down while higher thresholds may lead to multiplicity ofequilibria. Moreover, there are complex network effects. One bank's conversionmay trigger further conversions - or prevent them, depending on theconstellations of asset values and conversion triggers.

Contingent Capital with Stock Price Triggers in Interbank Networks