Models of systemic risk in financial networks

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Since the 2007-08 financial crisis, systemic risk the risk of large scale or even catastrophic disruptions of global financial markets - has become an active area of research worldwide. In this rich and complex subject, prediction of crises is the central, contentious issue. My research, starting in 2008, is summarized in a recent book [“Contagion! Systemic Risk in Financial Networks”] that is a roadmap to the field of financial stability. The book models crises in a network of banks interconnected by channels that transmit damaging shocks that may develop into domino-like “cascades” of bank defaults, bank depositor runs and asset fire sales.******Such cascade models give results about the global system inferred from the structure and behaviour of its nodes (“banks”) and edges (“interbank exposures”). “Percolation logic”, a line of network thinking that combines intuition from condensed matter physics and probability, leads to formulas for the ultimate size and impact of the cascade. These formulas hold in the limit of large networks, and on smaller networks give quantitative agreement with statistical results observed in simulation-based computations.******The proposal will strengthen and broaden the cascade framework introduced in the book, with two main objectives. First, the project will simulate and develop analytical methods for new families of random cascade models that distill essential aspects of bank behaviour, especially the intertwining of two or more channels. Resulting formulas for crisis size and impact are the basis for a mathematical laboratory for understanding stability in real financial networks such as the Canadian banking system. ******The second objective is to study the strategic behavior of banks under regulatory constraints, acting in a market of illiquid assets. This core problem in financial mathematics also relates to the fire sale channel of financial contagion where stressed banks that sell their fixed assets on a large scale create downward price spirals and system-wide deleveraging that is key in all financial crises. ******Studying optimal bank strategies will improve understanding of how liquidity and bank behaviour should be built into cascade mechanisms in systemic risk models. The new analytical methods for cascade models will yield the type of formulas that have been observed to be “unreasonably effective” in quantifying network stability. This research will lead to tools for finance practitioners, for example to test the effect of changes in Canadian regulations on the stability of our banking network. Other network scientists will find these methods insightful for understanding tipping points and phase transitions, particularly those associated with vulnerabilities of Canadian society such as the propagation of infectious diseases and the breakdown of power grids.**