A Multi-Period Bank-Run Model for Liquidity Risk

Abstract

We present a new dynamic bank run model for liquidity risk where a financial institution finances its risky assets by a mixture of short-and long-term debt. The financial institution is exposed to insolvency risk at any time until maturity and to illiquidity risk at a finite number of rollover dates. We compute both insolvency and illiquidity default probabilities in this multiperiod setting using a structural credit risk model approach. Firesale rates can be determined endogenously as expected debt value over current asset value. Numerical results illustrate the impact of various input parameters on the default probabilities.

Endogenous Credit Spreads and Optimal Debt Financing Structure in the Presence of Liquidity Risk

“…This default mechanism significantly differs from that in Liang et al . (, ) but bears some similarities to Schroth et al . () in which a run is triggered when the short‐term rate hits a given threshold.…”

“…This is different to the setting in Liang et al (, ) where creditors, who run on the financial institution at some time point, cannot return at a later time point. In that case creditors have to optimise over all remaining time periods.…”

“…If the short-term debt rates become too high, effectively shortterm creditors run on debt and the firm defaults due to illiquidity. This default mechanism significantly differs from that in Liang et al (2015Liang et al ( , 2014 but bears some similarities to Schroth et al (2014) in which a run is triggered when the short-term rate hits a given threshold. A main difference to our paper is that we consider a deterministic debt structure with two different types of debt which allows us to determine an optimal short-to-long-term debt ratio whereas Schroth et al (2014) assume a staggered debt structure such that only the average debt maturity can be specified.…”

“…In Morris and Shin (2010) the authors focus on a two-period setting where short-term creditors face a binary decision in terms of global games at an interim time point. Liang et al (2014Liang et al ( , 2015 combine ideas of global games with the dynamic coordination problems and derive debt run barriers such that creditors decide to withdraw their funding if the firm's asset value falls below this barrier. While these approaches assume constant short-term spreads, in this paper we develop a model that allows a firm to adjust to deteriorations in asset value and overall market conditions by offering credit spreads that induce creditors to prolong their funding.…”

“…Thus, creditors base their investment decision only on their potential returns over the lifetime of the current contract. 10 This is different to the setting inLiang et al (2014Liang et al ( , 2015 where creditors, who run on the financial institution at some time point, cannot return at a later time point. In that case creditors have to optimise over all remaining time periods.…”