Empirical Validation of the Merton Model: A Cointegration Analysis of Market- and Model-Implied Bond Prices

Abstract

Previous research indicates that structural credit risk models along the lines of Merton fail to match the size of empirically observed credit spreads, a result that is known as the ‘credit spread puzzle’. However, the significance of such models may equally be given by alternative quality criteria. In this paper, we propose that the Merton model instead may be able to replicate the stochastic trends exhibited by the market and thus form a cointegrating equilibrium with it. As such, the Merton model would still provide usable predictions with respect to mispricing in the market and correction of such disequilibrium. To test the hypothesis of cointegration with the market, we consider bonds of two public companies that have ideal capital structures for making predictions in a Merton model setting. The cointegration modelling is done with a single-equation approach according to Engle & Granger as well as the multi-equation approach of Johansen. While prices are the primary variable of interest, we also derive yields and spreads in order to account for potential trends of prices to face value at maturity. We find that cointegration is present for the company with the capital structure that most closely matches the Merton framework. For prices, this cointegration equilibrium includes a linear time trend, presumably due to differentially fast trending to face value at maturity. For the other company, no evidence of cointegration is found, though predictive time series models in first differences can still be built with help of the Merton model. In both cases, the Merton model time series Granger causes the market time series, thereby providing evidence that financial analysts make use of the Merton model when quoting prices in the market. Finally, the forecasting performance of these time series models is benchmarked against a simple random walk model, showcasing limited out-of-sample predictive validity as a result. Overall, our findings provide evidence for the relevance of structural credit risk models such as the Merton model, though in a limited setting with ideal capital structures.