Credit Risk: The Structural Approach Revisited

Abstract

In Merton’s seminal article on credit risk (1974), corporate bonds are viewed as derivatives based on the value of the firm; the latter is implicitly assumed to be a tradable asset. An unavoidable consequence of this approach is that the growth rate of the firm plays no rôle in the pricing of corporate bonds, as it is wiped out by the change to the risk-neutral measure.

We revisit the above structural approach to credit risk, taking the shares of the firm as the basic tradable asset. A difficulty arises from the fact that the value of the assets of the firm is not directly related to the value of its shares; this is resolved by constructing a model in which both quantities derive from the profits of the firm. A simple formula for the profits is derived by making certain assumptions on the structure of the firm, and this yields explicit formulae for the share price and the value of the assets of the firm.

This construction allows us to identify the relevant risk-neutral measure in an unambiguous manner, and thus to price the defaultable bond as a functional of the profits. This leads to an Asian option type of problem.

It is a pleasure to thank John Appleby, Connor Griffin, Gabriella Iovino, Brian O’Kelly, Anatoly Patrick and Paul Quigley (all members of the DCU ‘Default Club’ of 1998-99) for stimulating discussions.