On Bias of Testing Merton's Model
by Hoi Ying Wong of the Chinese University of Hong Kong, and
November 8, 2004
Abstract: In the credit risk modeling literature, there are two different viewpoints towards the structural model of Merton. Many empirical tests show that the Merton model overestimates corporate bond prices substantially. However, there are other empirical works defensing that the Merton model is useful in predicting default and performs well in estimating deposit insurance fund. In this paper, we argue that the poor performance of the Merton model may be the consequence of using proxies in empirical studies. Specifically, we show theoretically that using sum of market value of equity and book value of corporate liabilities as a proxy for the market value of corporate assets generates significant bias of overestimating the asset values. It follows that the market value of corporate bond, as a risk-free bond less a put option on corporate asset, would be overestimated under the Merton approach. We propose that the asset values and volatilities are better estimated with maximum likelihood estimation (MLE). To support this claim, we conduct a simulation and an empirical study. Our empirical results document that the proxy overstates corporate assets by 28% on average. If MLE is adopted, the Merton model can overestimate or underestimate the bond prices with the average percentage error of 0.3%.
Keywords: Corporate Bond Pricing, Merton's Model, Maximum Likelihood Estimation.