Financial Asset Bubbles in Banking Networks

We consider a banking network represented by a system of stochastic differential equations coupled by their drift. We assume a core-periphery structure, where banks in the core hold a bubbly asset. Investments are modeled by the weight of the links, which is a function of the robustness of the banks. In this way, a preferential attachment mechanism of the banks in the periphery towards the core takes place during the growth of the bubble. We then investigate how the bubble distorts the shape of the network for both finite and infinitely large systems, assuming a nonvanishing impact of the core on the periphery. Due to the influence of the bubble, banks are no longer independent, and the strong law of large numbers cannot be directly applied to the average of banks' investments towards the periphery. This results in a term in the drift of the diffusions which does not average out, increasing systemic risk when the bubble bursts. We test this feature of the model by numerical simulations.