A New Approach for Firm Value and Default Probability Estimation Beyond Merton Models

Abstract

In this paper we present a new model to assess the firm value and the default probability by using a bivariate contingent claim analysis and copula theory. First we discuss an unfeasible case, given the current derivative market on corporate bonds, which involves univariate digital options to compute the risk neutral probabilities. We then discuss a feasible model, which considers risky interest rates, instead. Moreover, we develop in this framework a new methodology to extract default probabilities from stock prices, only, going beyond the standard KMV-Merton model. Besides, the non-observability of the Merton model's state variable requires numerical methods, but the results can be unstable with noisy risky data. We show how the null price can be used as a useful barrier to separate an operative firm from a defaulted one, and to estimate its default probability. We then present an empirical application with both operative and defaulted firms to show the advantages of our approach.

Keywords: Firm value, No arbitrage, Structural models, Bivariate option, Copula, Default Probability

JEL Classification: G12, G30, G32