Valuing Corporate Liabilities When the Default Threshold is not an Absorbing Barrier

This paper studies the impacts of delays beyond the default event on the ex ante pricing of corporate liabilities and credit spreads. Such delays are often granted by courts within domestic bankruptcy codes. A Black–Scholes–Merton–Cox type framework is developed to account for both the subordination and the possible convertibility of debt to equity. In this structural approach, the firm assets value is allowed to cross the default barrier without causing an immediate liquidation. One shows that all the liquidation procedures based on the time spent by the firm in financial distress are bounded by a couple of ideal procedures. Interestingly, these latter lead to quasi-analytical pricing formulae for the corporate liabilities. We adapt and extend the analytical formulae introduced by Chesney et al. (1996) in the context of Parisian options, to derive these two bounds. We then conduct extensive numerical simulation. Among other results, experiments mainly conclude that the credit spreads increase or decrease monotonically w.r.t. the extra time granted beyond default, depending on the way the considered bond is secured or subordinated to others. Overall, this article complements François and Morellec (2002) who examine whether Chapter 11 of the US Bankruptcy procedure impacts on capital structure choices and the strategic decision to default in lines of Leland (1994).