Bank Risk Dynamics and Distance to Default

Working Paper: NBER ID: w25807

Authors: Stefan Nagel; Amiyatosh Purnanandam

Abstract: We adapt structural models of default risk to take into account the special nature of bank assets. The usual assumption of log-normally distributed asset values is not appropriate for banks. Typical bank assets are risky debt claims, which implies that they embed a short put option on the borrowers’ assets, leading to a concave payoff. This has important consequences for banks’ risk dynamics and distance to default estimation. Due to the payoff non-linearity, bank asset volatility rises following negative shocks to borrower asset values. As a result, standard structural models in which the asset volatility is assumed to be constant can severely understate banks’ default risk in good times when asset values are high. Bank equity payoffs resemble a mezzanine claim rather than a call option. Bank equity return volatility is therefore much more sensitive to big negative shocks to asset values than in standard structural models.

Keywords: No keywords provided

JEL Codes: G01; G21; G38

Causal Claims

Cause	Effect
traditional models that assume lognormally distributed asset values (C58)	significant underestimation of default risk in favorable economic conditions (G33)
low observed equity volatility (G17)	misleading indication of default risk (G33)
modified model predicts that bank asset volatility rises when borrower asset values fall (E44)	non-linear relationship between asset values and default risk (G19)
modified model's risk-neutral default probabilities are substantially higher than those predicted by the Merton model (G33)	higher probability of default in favorable conditions (G33)
Merton model's assumption of constant asset volatility (C58)	severe underestimations of bank default risk during good times (G21)
modified model captures the dynamics of default risk more accurately (G33)	aligns better with empirical data (C52)