Systemic risk: the dynamics of model banking systems

Abstract

The recent banking crises have made it clear that increasingly complex strategies for managing risk in individual banks have not been matched by corresponding attention to overall systemic risks. We explore some simple mathematical caricatures for 'banking ecosystems', with emphasis on the interplay between the characteristics of individual banks (capital reserves in relation to total assets, etc.) and the overall dynamical behaviour of the system. The results are discussed in relation to potential regulations aimed at reducing systemic risk.

Systemic risk in banking ecosystems

“…Much of the essential findings of such studies can be captured, and made more transparent, by a 'mean-field' approximation in which each bank has exactly average behaviour 27 . This means all banks are the same size (rescaled to 1), every bank is linked to exactly z others, all loans have the same magnitude, w, as do the capital reserves, c, and the ratios of loans to total assets, h.…”

“…Such market liquidity shocks are conventionally and sensibly represented by discount factors that, for a given asset class, are proportional to the number of failing banks holding the asset. This may be generalized to distinguish between strong liquidity shocks, associated with discounting specific asset classes, and weak liquidity shocks, resulting from the expectation of further defaults or a more general loss of confidence 27 . In all cases and in sharp contrast to the attenuation in interbank loan shocks, liquidity shocks amplify as more banks fail.…”

Rollover Risk, Network Structure and Systemic Financial Crises

“…May et.al (2008), Haldane (2009) and Schweitzer et al (2009) highlight the importance of developing models of financial system resilience using more general techniques and insights from the literature on networks and complex systems. Recent analyses in this vein include May and Arinaminpathy (2010), Gai and Kapadia (2010), and Gai et.al (2011). Although these models allow for an arbitrary number of financial institutions, the underlying topology of interactions and the balance sheets of the intermediaries are static.…”

Networks and webs in ecosystems and financial systems

“…The subsequent failure of some major financial institutions, and the consequent propagation of shocks throughout the banking system, have prompted a rapid rise in studies of the dynamics of 'toy models' of banking networks [20][21][22][23][24][25], along with exploration of possible implications for better regulation of the system [26][27][28][29].…”