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Estimating Merton's Model by Maximum Likelihood with Survivorship Consideration

by Jin-Chuan Duan of the University of Toronto,
Geneviève Gauthier of HEC (Montréal),
Jean-Guy Simonato of HEC (Montréal), and
Sophia Zaanoun of HEC (Montréal)

May 10, 2005

Abstract: One critical difficulty in implementing Merton's (1974) credit risk model is that the underlying asset value cannot be directly observed. The model requires the unobserved asset value and the unknown volatility parameter as inputs. The estimation problem is further complicated by the fact that typical data samples are for the survived firms. This paper applies the maximum likelihood principle to develop an estimation procedure and study its properties. The maximum likelihood estimator for the mean and volatility parameters, asset value, credit spread and default probability are derived for Merton's model. To our knowledge, this paper is the first to address the survivorship issue as well as the first to apply the maximum likelihood method to credit risk assessment in a portfolio context. A Monte Carlo study is conducted to examine the performance of this maximum likelihood method. An application to real data is also presented.

JEL Classification: C22.

Keywords: Credit risk, maximum likelihood, option pricing, Monte Carlo simulation.

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