Merton for Dummies: A Flexible Way of Modelling Default Risk

One of the most popular approaches to default probability estimation using market information is the Merton [1974] approach. By explicitly modelling a firm's market value, market value volatility and liability structure over time using contingent claims analysis the Merton model defines a firm as defaulted when the firm's value falls below its debt. In this paper we show how a simplified "spread sheet" version of the Merton model produces distance to default measures similar to the original Merton model. Moreover, when applied to a sample of US firms, the simplified model gives a relative ranking of firms that is essentially unchanged compared to the Merton model. Our paper has three main implications. First, the simplicity of our model makes it suitable as a framework for a more elaborate dynamic modelling of volatility and leverage ratios with the aim of capturing the dynamic nature of default risk suggested by empirical evidence. At the same time, in the model's most simple version, distance to default can be calculated very quickly and intuitively (on the back of an envelope). Second, the default probability's insensitivity to the leverage ration at high levels of debt makes it possible to apply the model to banks and other highly leveraged firms without exact knowledge of their leverage ratios. Third, the model can be applied to any firm regardless of its level of riskiness without estimation problems.