Beyond Merton: Multi-Dimensional Balance Sheet in Default Modeling

Nearly half a century after Merton’s 1974 paper, the basic framework of modeling a company’s default risk in terms of one-dimensional variable, the total asset value, with fixed debt level has remain unchanged among the work by academic and quantitative modeling community. Under such simplification, the model is unable to correctly defined the state of default, which is a state of negative cash. But more importantly, Merton’s one-dimensional model cannot incorporate the fundamental principle of balanced balance sheet, and thus unable to generate the rich dynamics followed by a company’s multi-dimensional financial state. This article presents an example of 2-dimensional balance sheet that is still analytically solvable to demonstrate the multi-dimensional kinematics of a company’s financial state, and the much more nontrivial default dynamics as a result. The idealized example is for demonstrate purpose only, but the methodology has been extended to higher-dimensional balance sheet to model actual companies and forecast default with computerizable numerical and simulative algorithms.