Robustness of Distance-to-Default

Distance-to-default is a remarkably robust measure for ranking firms according to their risk of default. The ranking seems to work despite the fact that the Merton model from which the measure is derived produces default probabilities that are far too small when applied to real data. We use simulations to investigate the robustness of the distance-to-default measure to different model specifications. Overall we find distance-to-default to be robust to a number of deviations from the simple Merton model that involve different asset value dynamics and different default triggering mechanisms. A notable exception is a model with stochastic volatility of assets. In this case both the ranking of firms and the estimated default probabilities using distance-to-default perform significantly worse. We therefore propose a volatility adjustment of the distance-to-default measure, that significantly improves the ranking of firms with stochastic volatility.