Bank Risk Dynamics and Distance to Default

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.

What's Different about Bank Holding Companies?

“…He and Krishnamurthy (2012) provides a model with a specialist desk similar to a trading desk that is subject to capital constraints. Nagel and Purnanandam (2016) consider a bank with overlapping loans and no trading desk in which the underlying projects, financed by these loans, follow a stochastic process. They then value the option value of loans, debt and equity.…”

The risk spiral: The effects of bank capital and diversification on risk taking

“…To our knowledge this paper is the first to incorporate simultaneously three important aspects of bank assets. First, we assume that bank assets are composed of risky debt claims (Dermine and Lajeri, 2001;Chen, Ju, Mazumdar, and Verma, 2006;Nagel and Purnanandam, 2015).…”

“…Second, we consider the effect of risk shifting on the equilibrium level of asset risk as well as on the bank's cost of default (Peleg Lazar and Raviv, 2017). Finally, we assume that bank assets are a portfolio of loans to borrowers that have different leverage and correlations coefficients between the returns on their assets (Flannery, 1989;Gornall and Strebulaev, 2018;Nagel and Purnanandam, 2015).…”

“…However, the approach does not consider three important aspects of bank assets. First, commercial bank assets are often in the form of debt -loans and bonds -with a limited upside (Dermine and Lajeri, 2001;Gornall and Strebulaev, 2018;Nagel and Purnanandam, 2015). Second, bank assets are composed of a portfolio of loans to different borrowers with varying leverage, asset risk, and asset correlation (Flannery, 1989;Chen, Ju, Mazumdar, and Verma, 2006).…”

“…We assume that a bank's assets are a portfolio of loans to corporations. The borrowers' assets, which serve as collateral for the loans, follow a geometric Brownian motion (Gornall and Strebulaev, 2018;Nagel and Purnanandam, 2015). Due to the legal limited liability of stockholders, a borrower's stock value has a lower limit of zero.…”