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

Abstract

When a default payment occurs, many bankruptcy codes favour firm continuation against claims reimbursement i.e. immediate liquidation of the firm assets. Hence, safety covenants (allowing bondholders to bankrupt the firm) are violated. Default and liquidation cannot be considered as equivalent events anymore. And the absorbing barrier, first introduced by Black-Cox (1976) and used as an immediate liquidation threshold in structural models (Leland (1994), Longstaff-Schwartz (1995), Leland-Toft (1996)) largely over-estimates creditors rights.

This paper aims at reconciling the classical contingent claims analysis with this observed deviation from net-worth covenants. The assets value is now allowed to pass through the default threshold without causing the usual immediate liquidation. While some procedures based on excursion and occupation times may be designed, it is shown that only the latter sufficiently accounts for past financial distresses. Complex corporate securities (including subordinated and convertible debt) are then priced within an extended framework a la Black-Cox-Scholes-Merton. Depending on the retained liquidation procedure, analytical formulae of Chesney-Jeanblanc-Picque-Yor (1995) for valuing parisian options must be extended or not.

Keywords: Bankruptcy procedures, Debt pricing, Default, Liquidation

JEL Classification: G130, A910