Bank Risk Dynamics and Distance to Default

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. 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 negative shocks to asset values than in standard structural models. ∗We are grateful for conversations with Stephen Schaefer. †Ross School of Business and Department of Economics, University of Michigan, 701 Tappan St., Ann Arbor, MI 48109, e-mail: [email protected] ‡Ross School of Business, University of Michigan, 701 Tappan St., Ann Arbor, MI 48109, e-mail: [email protected]