Modelling default risk with occupation times

This paper develops a semi-analytic pricing formula, easily implemented via quadrature, for a structural model based on occupation times that contains both the Merton and Black-Cox models as limiting cases. In the model liquidation is triggered as soon as the firm's asset value has spent a prespecified amount of time below the default barrier. Surprisingly, we find that the value of the firm's debt (i) need not be monotone in the length of the grace period and (ii) need not lie between the limiting Merton and Black-Cox values.