European Puts, Credit Protection, and Endogenous Default

Abstract

In a default corridor [0,B] that the stock price can never enter, a deep out-of-the-money American put replicates a pure credit contract (Carr and Wu, 2011). Assuming discrete (one-period-ahead predictable) cash flows, we show 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 credit-contract replicating put is not American, but rather European. Specifically, 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.

Keywords: equity puts, endogenous default, default corridor, credit risk, insurance

JEL Classification: G10, G12, G13