The Mills Ratio and the behavior of redeemable bond prices in the Gaussian structural model of corporate default

This paper shows that forward default intensities in the Black and Cox (1976) model of corporate default can be expressed in terms of the Mills Ratio (Mills, 1926). The behaviour of the forward default intensity and hence the survivorship functions then follows from inequalities that are satisfied by this ratio. This allows me to analyze the effect of the firm’s distance to default, growth rate and volatility upon the value of its debt. These results can be used to analyze the comparative static properties of other models of corporate default and perhaps other first passage time models.