Estimating Merton's Model by Maximum Likelihood with Survivorship Consideration

25 Pages Posted: 23 Jun 2004

See all articles by Jin-Chuan Duan

Jin-Chuan Duan

National University of Singapore (NUS) - Business School and Risk Management Institute

Jean-Guy Simonato

HEC Montréal

Geneviève Gauthier

HEC Montreal - Department of Decision Sciences; HEC Montreal - Department of Management Sciences

Sophia Zaanoun

HEC Montreal

Date Written: March 2004

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. A Monte Carlo study is conducted to examine the performance of this maximum likelihood method. An application to real data is also presented.

Suggested Citation

Duan, Jin-Chuan and Simonato, Jean-Guy and Gauthier, Genevieve and Zaanoun, Sophia, Estimating Merton's Model by Maximum Likelihood with Survivorship Consideration (March 2004). EFA 2004 Maastricht Meetings Paper No. 4190. Available at SSRN: https://ssrn.com/abstract=557088 or http://dx.doi.org/10.2139/ssrn.557088

Jin-Chuan Duan (Contact Author)

National University of Singapore (NUS) - Business School and Risk Management Institute ( email )

1 Business Link
Singapore, 117592
Singapore

Jean-Guy Simonato

HEC Montréal ( email )

3000, chemin de la Cote-Sainte-Catherine
Service de l'enseignement de la finance
Montreal, Quebec H3T 2A7
Canada
514-340-6807 (Phone)
514-340-5632 (Fax)

Genevieve Gauthier

HEC Montreal - Department of Decision Sciences ( email )

3000 Côte-Sainte-Catherine Road
Montreal, QC H2S1L4
Canada

HEC Montreal - Department of Management Sciences ( email )

Montreal, Quebec H3T 2A7
Canada

Sophia Zaanoun

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H3T 2A7
Canada

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