This paper presents a dynamic model of banking interactions, which uses interbank connections to study the stability of the banking system. The dynamic model extends previous work on network models of the banking system taking inspiration from large scale, complex, interconnected systems studied within the domain of engineering. The banking system is represented as a network where nodes are individual banks and the links between any two banks consist of interbank loans and borrowing. The dynamic structure of the model is represented as a set of differential equations, which, to the best of our knowledge, is an original characteristic of our approach. This dynamic structure not only allows us to analyse systemic risk but also to incorporate an analysis of control mechanisms.
Uncertainty is introduced in the system by applying stochastic shocks to the bank deposits, which are assigned as an exogenous signal. The behaviour of the system can be analysed for different initial conditions and parameter sets. This paper shows some preliminary results under different combinations of bank reserve ratios, bank capital sizes and different degrees of bank inter-connectedness.
The results show that both reserve ratio and link rate have a positive effect on the stability of the system in the presence of moderate shocks. However, for high values of the shocks, high reserve ratios may have a detrimental effect on the survival of banks.
In future work, we will apply strategies from the domain of control engineering to the dynamic model to characterise more formally the stability of the banking network
