European Puts, Credit Protection, and Endogenous Default

In a default corridor [0; B] that the stock price can never enter, a deep out-of-the-money American put option replicates a pure credit contract (Carr and Wu, 2011). Assuming discrete (one-period-ahead predictable) cash flows, we show that an endogenous credit-risk model generates, along with the default event, a default corridor at the cash-outflow dates, where B > 0 is given by these outflows (i.e., debt service and negative earnings minus dividends). In this endogenous setting, however, the put replicating the credit contract is not American, but European. Specifcally, the crucial assumption that determines an endogenous default corridor at the cash-outflow dates is that equityholders' deep pockets absorb these outflows; that is, no equityholders's fresh money, no endogenous corridor.