A Multiperiod 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.

Do bank activities and funding strategies of foreign and state‐owned banks have a differential effect on risk‐taking in Central and Eastern Europe?

“…Liang et al. () develop a dynamic structural bank run model for liquidity risk, in which a financial institution finances its risky assets using a mixture of short‐ and long‐term debt. In their framework, the short‐term creditors of the financial institution can choose not to renew their funding at certain rollover dates.…”

Bank excess reserves in emerging economies: A critical review and research agenda

“…Agenor et al (2004) identify the demand for a bank's precautionary excess reserves as a function of the penalty rate, cash-deposit ratio deviation, output deviation, foreign exchange exposure and their lags. However, this framework does not consider a bank's credit risk, which is argued to be positively related to liquidity risk (Liang, Lutkebohmert, & Xiao, 2013;Morris & Shin, 2009). Once liquidity risk increases, banks will demand more excess reserves to buffer against uncertainty (Baltensperger, 1972).…”

When do creditors with heterogeneous beliefs agree to run?

“…A major merit of the recent work in this direction, e.g. [24,14,18,19], is the focus on the interplay between insolvency and illiquidity risk (in the sense of funding illiquidity risk). Here we do not model insolvency risk, but we push further the analysis of the strategic interaction among creditors leading to funding illiquidity.…”

“…However, unlike in previous work, the relevant quantity in our model is the liquid net worth, and not the net worth. [18,19] avoid the equilibrium ambiguity by assuming an exogenous model for the bank run probability. In our analysis, this model assumption is not needed, and we obtain the bank run probability endogenously from the creditors' beliefs about the borrower's fundamentals.…”

“…In our analysis, this model assumption is not needed, and we obtain the bank run probability endogenously from the creditors' beliefs about the borrower's fundamentals. Moreover, we do not assume a "representative creditor" as in [18,19], but we allow heterogeneous beliefs of creditors about the prospects of the borrower. The heterogeneity of economic creditors is a phenomenon that has important implications beyond the problems discussed in this paper.…”