Default robustness and worst-case losses in financial networks

We analyze the resilience and worst-case losses in a financial network of banks linked by mutual liabilities and shared exposures to external assets. Abrupt asset price changes lead to simultaneous shocks to bank balance sheets, potentially triggering cascades of defaults. In this context, we introduce first the concept of default resilience margin,, defined as the maximum amplitude of asset prices fluctuations that the network can sustain without generating defaults. Such threshold value is computed by considering two different measures of price fluctuations, one based on the maximum individual variation of each asset, and the other based on the sum of all the asset’s absolute variations. For any price perturbation having amplitude no larger than, the network absorbs the shocks and remains free of defaults. When the perturbation amplitude goes beyond the level, however, defaults may occur. We assume that external liabilities have higher priority than interbank claims, thereby distinguishing between banks that default on obligations to other banks and those that are fully insolvent, i.e., unable to meet even their external obligations. We propose an explicit method to determine the upper bound on shock amplitude, below which such insolvencies do not occur–that is, all banks are able to fulfill their external liabilities, though some may default on their interbank obligations. For each shock amplitude, we show how to compute the worst-case systemic loss, that is, the total financial network shortfall under the worst-case scenario of price variation of given magnitude.