Merton's Default Risk Model for Private Company

TL;DR

This paper extends Merton's default risk model to private companies by integrating the dividend discount model, deriving closed-form formulas for valuation and default probability, and proposing ML estimators and EM algorithm for parameter estimation.

Contribution

It develops a novel structural model for private companies using DDM, providing analytical formulas and estimation methods not previously available.

Findings

Closed-form formulas for equity and liability values

Analytical default probability formulas

ML estimators and EM algorithm for model parameters

Abstract

Because the asset value of a private company does not observable except in quarterly reports, the structural model has not been developed for a private company. For this reason, this paper attempt to develop the Merton's structural model for the private company by using the dividend discount model (DDM). In this paper, we obtain closed--form formulas of risk--neutral equity and liability values and default probability for the private company. Also, the paper provides ML estimators and the EM algorithm of our model's parameters.