Robustness of distance-to-default

Abstract

Distance-to-default (DD) is a measure of default risk derived from observed stock prices and book leverage using the structural credit risk model of Merton (1974). Despite the simplifying assumptions that underlie its derivation, DD has proven empirically to be a strong predictor of default. We use simulations to show that the empirical success of DD may well be a result of its strong robustness to model misspecifications. We consider a number of deviations from the Merton model which involve different asset value dynamics and different default triggering mechanisms. We show that, in general, DD is successful in ranking firms' default probabilities, even if the underlying model assumptions are altered. A possibility of large jumps in asset value or stochastic volatility challenge the robustness of DD. We propose a volatility adjustment of the distance-to-default measure that significantly improves the ranking of firms with stochastic volatility, but this measure is less robust to model misspecifications than DD. * Support from the Center for Financial Frictions (FRIC), grant no. DNRF102, is gratefully acknowledged. Cathrine Jessen also thanks the Danish Council for Independent Research | Social Sciences for financial support. We are grateful for comments from our discussant at the International Conference on Financial Regulation and Systemic Risk in Paris, André Lucas, and an anonymous referee.

Measuring sovereign credit risk using a structural model approach

“…From Engelmann et al (2003) and Jessen and Lando (2015), our hypothesis is H 0 : AUC 1 ¼ AUC 2 for any two of our three models. The test statistic is…”

“…To compare the performance of the three models based on our sovereign balance sheet, we follow Jessen and Lando (2015) using ROC, 12 the Mann-Whitney U-test, and Spearman's q to test whether our model CDS prices can reflect the information regarding sovereign risk. Since Spearman's q is a measure of rank correlation, a high Spearman's q implies high area under the curve (AUC).…”

“…The unknown variables and parameters in the Merton model and BT model are estimated by the transformed-data maximum likelihood estimation (MLE) method proposed by Duan (1994Duan ( , 2000, Duan et al (2003Duan et al ( , 2004; the variables in the LT model are estimated by the mixed maximization-maximization (MM) algorithm proposed by Forte (2011) and Forte and Lovreta (2012). Finally, we apply the Spearman's rank correlation coefficient (Spearman's q) and the receiver operating characteristic (ROC) test adopted by Engelmann et al (2003) and Jessen and Lando (2015) to examine the model performance.…”

The relationship between distance-to-default and CDS spreads as measures of default risk

“…In addition to our promising results for the distance-todefault, the fact that the D2D's assumptions have been shown to be quite robust to deviations (Jessen and Lando, 2015) makes this default risk measure a very good alternative to the most commonly used market based early warning indicator. As the D2D is also available for a much broader range of banks and not only the largest ones, the D2D is also a better measure from a practical point of view.…”

“…The derivation of D2D assumes, for example, that there are no market frictions and that the fi rm's asset value follows a geometric Brownian motion, which might not be true all the time. Jessen and Lando (2015) studied the robustness of D2D on deviations from the Merton model assumptions. They found that D2D is a robust measure for ranking different fi rms according to their default risk despite deviations from most of the assumptions, except for large jumps in the asset value process or if it has stochastic volatility.…”