In "Financial Contagion" (2000), Allen and Gale showed how an interbank market can be affected by regional liquidity shocks, and how a local bank crisis can become global when banks are interconnected through deposits. The purpose of this thesis is to analyze the robustness of different interbank market structures towards regional liquidity shocks. We formulate a mathematical framework for theanalysis and show how to find optimal deposits between banks by solving a minimum flow distribution problem on a network with the underlying graph representing the market structure. We use a breadth-first search (BFS) algorithm, which takes the optimal deposits between banks as input parameter, to traverse through the graph and analyze the effects of a regional liquidity shock.
Central results include showing that a maximum correlation linear graph is the least robust market structure, and we derive an optimality result for the k-regular bipartite graph. Robustness properties of other graph structures are also found. The results are shown by deriving properties of the minimum flow distribution problem, which are used for the analysis of the BFS algorithm.
The thesis also include numerical simulations, which confirm and illustrate the theoretical results, and MATLAB program code written specifically to solve the Allen and Gale model for different underlying graph structures.