Using the Black Scholes Merton contingent claims approach to the valuation of corporate debt to model default risk: Why Moody’s Investor Services bought KMV Corporation.
by
Lyle C Gurrin
Corporate Finance, BHP Billiton Limited
Coauthors: Edmund RF Bosworth (Capital Management, Westpac Banking Corporation)

In assessing the credit risk of publicly listed firms there has recently been a shift away from traditional statistical models of default risk based on accounting measures towards structural models that use stock market prices. The latter were originated by Merton, who introduced a contingent claims approach to the valuation of corporate debt. Here shareholders are viewed as having paid the market value of the firm’s equity in exchange for a call option on the firm’s assets with strike price the face value of the firm’s debt. Consequently, a firm will default when the value of its assets is less than the value of its debt.

By assuming that the market value of a firm’s assets follows a geometric Brownian motion stochastic process, the Black Scholes option pricing model can be used to solve for the unknown market value and volatility of the firm’s assets by establishing their relationship with the observable market value and volatility of the firm’s equity. Standardising the difference between the random asset value and the debt commitment for a given time horizon generates a measure of credit risk known as the “distance to default”, which is mapped empirically using historical data to a default probability.

There has been intense debate as to whether the output of a Merton model can be enhanced by combining it with Moody’s debt ratings or other accounting ratios. Research by Kealhofer and Kurbat (2002) of KMV Corporation, the organisation that championed the Merton approach, appears to show that hybrid models reduce predictive power, although staff from Moody’s and CitiGroup disagree (Risk February 2002). The controversy centres on how best to compare two credit rating scales using a single observed distribution of defaults and the appropriate specification of the null hypothesis that an alternative rating scale does not provide additional predictive information. The debate reached a stunning climax in February this year when Moody’s Investor Services bought KMV for $US 210 million. We’ll provide an industry perspective on this debate and speculate on the future of modelling default risk with Moody’s as the “global credit risk champion”.

Date received: April 23, 2002