Contingent Capital with Stock Price Triggers in Interbank Networks

TL;DR

This paper analyzes the conditions for the existence and uniqueness of equilibrium prices in a banking network with contingent convertible bonds triggered by stock prices, highlighting complex network effects and stability issues.

Contribution

It introduces a model examining equilibrium conditions in interbank networks with stock-triggered convertible bonds, revealing when unique or multiple equilibria occur.

Findings

Unique equilibrium exists when conversion thresholds make bondholders indifferent.

Lower thresholds can cause non-existence of equilibrium.

Higher thresholds may lead to multiple equilibria and complex network effects.

Abstract

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