Optimal Payments to Connected Depositors in Turbulent Times - A Markov Chain Approach

Ddvid Csercsik,Hubert Janos Kiss

doi:10.2139/ssrn.2784692

Abstract

We propose a discrete time probabilistic model of depositor behavior which takes into account the information ﬂow among depositors. In each time period each depositors’ current state is determined in a stochastic way, based on its previous state, the state of other connected depositors and the strategy of the bank. The bank oﬀers payment to impatient depositors who accept or decline them with certain probability, depending on the oﬀered amount. The connections between depositors aﬀect the evolution of the state trajectory as well: the more other connected depositors demand money from the bank, the larger is the probability that the depositor turns also impatient. Our principal aim is to see how are the optimal oﬀers of the bank if it wants to keep the expected chance of a bank run under a certain level and minimize its expected payments, while taking into account the connection structure of the depositors. We show that in the case of the proposed model this question results in a nonlinear optimization problem with nonlinear constraints, and that the method is capable of accounting for time-varying resource limits of the bank. Optimal oﬀers increase a) in the degree of the depositor; b) in the probability of being hit by a liquidity shock, and c) the eﬀect of a neighboring impatient depositor.

Highlights

Banks and other financial intermediaries convert short-term liabilities into long-term and often illiquid assets, a process called maturity transformation
Liquidating the assets is generally costly; if many depositors or investors attempt to withdraw their funds from the bank or from other forms of financial intermediation, liquidity problems may arise that may spark a bank run and result in solvency problems through fire sales
We find that the lower is the probability of bank runs that a bank tolerates, the larger is the optimal offer, all other things held constant

Summary

Introduction

Banks and other financial intermediaries convert short-term liabilities into long-term and often illiquid assets, a process called maturity transformation. Liquidating the assets is generally costly; if many depositors or investors attempt to withdraw their funds from the bank or from other forms of financial intermediation, liquidity problems may arise that may spark a bank run and result in solvency problems through fire sales. If depositors anticipate such potential problems, it may in turn make them more prone to withdraw. In traditional bank run models [1, 2] banks are supposed to determine payment to those who withdraw as a result of a maximization problem.

Methods

Results

Conclusion