Decoding Financial Contagion: How Shocks Spread Through Banking Networks

'Contagion on Financial Networks' is a concept that combines financial mathematics, specifically stochastic differential equations, and network science to analyze how financial shocks spread through banking systems. It allows us to study the interconnectedness of banks and how the distress of one bank can affect others, potentially leading to a domino effect of defaults. By modeling these interdependencies, we can better understand and potentially mitigate systemic risks within the financial system. Further research explores varied network structures, going beyond the single probability 'p' mentioned, investigating the effects of clustering, core-periphery structures, and real-world network data.

According to Gai & Kapadia (2010), a bank remains solvent if its net assets, represented by the capital buffer K_i, are greater than zero. This is mathematically expressed as A^S – L^I = K_i > 0, where A^S represents the bank's total assets and L^I represents its total liabilities. These assets and liabilities include interbank assets (A^B), illiquid external assets (A^M), interbank liabilities (L^IB), and customer deposits (D_i). Further, the variables q (resale price of illiquid assets) and φ (the fraction of banks with obligations to any bank that has defaulted) play a crucial role. The bank's ability to cover its liabilities with its assets determines its solvency, especially when considering potential losses from distressed asset sales and the impact of defaulting counterparties.

The research suggests that the level of interconnectedness among banks plays a critical role in how financial shocks spread. Allen & Gale (2000) found that fully connected banks are more resilient to economic crises because shocks can be distributed evenly throughout the system, preventing any single bank from bearing the full impact. However, Gai & Kapadia (2010) also suggest that while interconnectedness can help absorb shocks, the specific structure of the network and the probability of links between banks significantly influence the extent of contagion. Greater connectivity leads to smaller impacts from individual shocks, however, a critical point can occur in which a specific range of probability values are optimal for bank solvency rates. Further research should model scenarios of network breakdown to see at which point the shock absorption fails.

Real-world events, such as epidemics or significant economic downturns, can significantly shift the dynamics of financial contagion. These events can cause unexpected and widespread shocks to the system, leading to increased uncertainty and potential fire sales of assets, which can further destabilize banks. Policy changes, shifts in investor sentiment, and technological disruptions can also impact the behavior of banking networks and the spread of financial distress. Additionally, the model makes several assumptions (such as the random construction of A^M and D_i) that may not be true in the real-world, and can impact the results.

Differentiating between interbank assets (A^B) and illiquid external assets (A^M) is crucial because they behave differently during a financial crisis. Interbank assets represent claims on other banks and are directly affected by the solvency of those banks. If a bank defaults, its interbank assets may become impaired, leading to losses for the banks that hold those assets. Illiquid external assets, such as mortgages, are less directly tied to the solvency of other banks but can lose value during a crisis if fire sales occur, driving down their resale price (q). The relative size and composition of A^B and A^M determine how a bank is affected by and contributes to financial contagion. Further, the model assumes each link is created with an independent probability p, however the asset types could correlate in reality.