The Structural Approach to Default Prediction and Valuation
Structural models of default risk are cause-and-effect models. From economic reasoning, we identify conditions under which we expect borrowers to default and then estimate the probability that these conditions come about to obtain an estimate of the default probability.
For limited liability companies, default is expected to occur if the asset value (i.e., the value of the firm) is not sufficient to cover the firm's liabilities. Why should this be so? From the identity
Asset value = Value of equity + Value of liabilities
and the rule that equity holders receive the residual value of the firm, it follows that the value of equity is negative if the asset value is smaller than the value of liabilities. If you have something with negative value, and you can give it away at no cost, you are more than willing to do so. This is what equity holders are expected to do. They exercise the walk-away option that they have because of limited liability and leave the firm to the creditors. As the asset value is smaller than the value of liabilities, creditors' claims are not fully covered, meaning that the firm is in default. The walk-away option can be priced with standard approaches from option pricing theory.
This is why structural models are also called option-theoretic or contingent-claim models. Another common name is Merton models, because Robert C. Merton (1974) first applied option theory to the problem of valuing a firm's ...