The Kealhoffer-Merton-Vasicek (KMV) model is derivative of Merton. Essentially, it codifies the calibration process and extends the framework to empirical distributions.
The following entry, Modeling Default Risk, contains one such passage regarding KMV’s parameterization of liabilities:
Oldrich Vasicek and Stephen Kealhofer have extended the
Black-Scholes-Merton framework to produce a model of default
probability known as the Vasicek-Kealhofer (VK) model. This model
assumes the firm’s equity is a perpetual option with the default point
acting as the absorbing barrier for the firm’s asset value. When the
asset value hits the default point, the firm is assumed to default.
Multiple classes of liabilities are modeled: short-term liabilities,
long-term liabilities, convertible debt, preferred equity, and common
equity. When the firm’s asset value becomes very large, the
convertible securities are assumed to convert and dilute the existing
equity. In addition, cash payouts such as dividends are explicitly
used in the VK model. A default database is used to derive an
empirical distribution relating the distance-to-default to a default
probability. In this way, the relationship between asset value and
liabilities can be captured without resorting to a substantially more
complex model characterizing a firm’s liability process.
Personally, I find that attempts to systemically implement KMV in the real world often fall short by attempting to introduce more precision than is practical, especially when one wishes to retain analytically desirable properties of plain vanilla Merton. When partitioning various types of assets and liabilities, for example, there may be different default probabilities assigned to different debt maturities and different classes of claims with or without maturity. Rather than introduce excessive complexity, I usually make simplifying assumptions such as grouping all non-current debt by average YTM and maturity and retaining assumptions regarding the log-normality of the processes.
In spite of its complexities, I believe that KMV’s canonical approach to structuring liabilities is instructive as to how one might decide to structure a similar model.