Systemic Risk in Financial Networks Revisited: Debt Dilution as a Backdoor Bail-In

Battle Count: 77

This paper is primarily relevant to systemic risk assessment, financial stability regulation, and bank resolution policy rather than quantitative trading strategies. However, understanding interbank network fragility and the role of gross vs. net positions could inform counterparty risk models, credit risk assessment for financial institutions, and macroprudential stress testing. The insights about dilutable debt and network topology could be relevant for trading desks managing exposure to financial institutions during stress periods.

The theoretical framework involves sophisticated mathematical tools: fixed-point theorems, Markov chain analysis, M-matrix theory, knapsack problem algorithms, and pairwise stability analysis. Implementing the model computationally would require solving systems of nonlinear equations (clearing vectors), constructing exponential networks with specific dominance parameters, and verifying pairwise stability conditions. The analytical proofs are complex, though the core equilibrium computation (clearing vector) is relatively straightforward for small networks.

The paper is purely theoretical with complete proofs provided in the appendix. All model parameters, equilibrium definitions, and propositions are fully specified. However, there is no code or numerical implementation provided. Reproducibility depends on verifying the analytical proofs. The worked examples (ring network, exponential network with 3 banks) are fully specified and can be independently verified.