In the literature, there are two theoretical approaches to the pricing of risky debt.
Both approaches take into account, credit spreads as a central component in their pricing
models and attempt to describe default processes. The credit spread is defined as the
difference between the yield of corporate bond and the associated yield on Treasury bonds
with the closest matching maturity.
In the structural approach,1 one makes explicit assumptions about the dynamics of a
firm’s assets, its capital structure, as well as its debt and shareholders. It is then assumed
that the firm defaults, if its assets are not sufficient to pay off the due debt. In this
situation, corporate liabilities can be considered as contingent claims on the firm’s asset.
The structural literature on credit risk starts with the paper by Merton (1974),
which applies the option pricing theory developed by Black and Scholes (1973) to the
modelling of a firm's debt. Notice that in this first category of models, defaults can only
happen at the maturity of zero coupon debt.
Other recent studies depart from Merton (1974) to include, for example, stochastic
interest rates (Longstaff and Schwartz, 1995; and Briys and de Varenne, 1997), stationary
leverage ratios (Collin-Dufresne and Goldstein, 2001) and the information contained in
stock market returns (Demchuk and Gibson, 2006). Also, Anderson and Sundaresan
(1996) examine violations of the absolute priority rule and strategic default. Zhou (2001)
introduces jumps in the asset value process. Although the second category of structural
models leads to more realism in the pricing of defaultable bonds, it introduces serious
drawbacks and analytical complexities. |