Government bailouts and default risks of a duopoly: strong bank versus weak bank

A duopolistic loan market includes a strong bank without the problem of early closure that opts out of government bailouts and a weak bank with this problem that participates in the bailout programmes of distressed loan purchases and direct equity injections. A direct implication of our framework is that the strong bank's equity will be priced as a standard call option, while the weak bank's equity will be priced as a down-and-out call option. We find that an increase in either bailout (i.e. distressed loan purchases and direct equity injections) directly decreases the weak bank's default risk but indirectly increases the strong bank's default risk. Accordingly, either bailout contributes to banking stability since the indirect positive effect insufficiently offsets the direct negative effect, giving an overall negative response of default risks to an increase in either bailout. Higher competition by shifting to quasi-competition from collusion increases banking stability under either bailout. Our analysis suggests that competition is aligned with the regulatory objective of improving stability.