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Journal of Credit Risk

Volume 1/Number 1, Winter 2004/05

Merton’s model, credit risk and volatility skews

John C. Hull Joseph L. Rotman School of Management, University of Toronto, 105 St George Street, Toronto, Ontario, Canada M5S 3E6; email: hull@rotman.utoronto.ca

Izzy Nelken Super Computing Consulting Group, 3943 Bordeaux Drive, Northbrook, IL 60062-2135 USA; email: izzy@supercc.com

Alan D. White Joseph L. Rotman School of Management, University of Toronto, 105 St George Street, Toronto, Ontario, Canada M5S 3E6; email: awhite@rotman.utoronto.ca

In 1974 Robert Merton proposed a model for assessing the credit risk of a company by characterizing the company’s equity as a call option on its assets. In this paper we propose a method for estimating the model’s parameters from the implied volatilities of options on the company’s equity. We use data from the credit default swap market to compare our implementation of Merton’s model with the traditional approach to implementation.


The assessment of credit risk has always been important to banks and other financial institutions. Recently, banks have devoted even more resources than usual to this task. This is because, under the proposals in Basel II, regulatory credit risk capital may be determined using a bank’s internal assessments of the probabilities that its counterparties will default.

One popular approach to assessing credit risk involves Merton’s (1974) model. This model assumes that a company has a certain amount of zero-coupon debt that will become due at a future time T. The company defaults if the value of its assets is less than the promised debt repayment at time T. The equity of the

We are grateful to Moody’s Investors Service for financial support and to GFI for making their data on credit default swap spreads available to us. We are also grateful to Jeff Bohn, Richard Cantor, Darrell Duffie, David Heath, Stephen Figlewski, Jerry Fons, David Lando, William Perraudin, Mirela Predescu, David Shimko (a referee), Roger Stein, Kenneth Singleton and workshop participants at Queens University, University of Toronto, York University, the Moody’s Academic Advisory Committee, an International Association of Financial Engineers event, an International Monetary Fund event, and the Risk Management Conference of the Chicago Board Options Exchange for helpful comments on earlier drafts of this paper. Needless to say we are fully responsible for the content of the paper.


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