A Multi-Period Bank Run Model for Liquidity Risk

We present a 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 liquidity risk as its short-term creditors have the possibility not to renew their funding at a finite number of rollover dates. Besides, the financial institution can default due to insolvency at any time until maturity. We compute both insolvency and illiquidity default probabilities in this multi-period setting. We show that liquidity risk is increasing in the volatility of the risky assets and in the ratio of the return that can be earned on the outside market over the return for short-term debt promised by the financial institution. Moreover, we study the influence of the capital structure on the illiquidity probability and derive that illiquidity risk is increasing with the ratio of short-term funding.