Models of systemic risk in financial networks

自2007-08年金融危机以来，系统性风险--即全球金融市场大规模甚至灾难性中断的风险--已成为全球范围内一个活跃的研究领域。在这个丰富而复杂的主题中，对危机的预测是一个核心而又有争议的问题。我的研究始于2008年，在最近的一本书[《传染病！金融网络中的系统性风险“]这是金融稳定领域的路线图。这本书对银行网络中的危机进行了建模，这些银行网络通过传递破坏性冲击的渠道相互连接，这些冲击可能会演变为银行违约、银行储户挤兑和资产大甩卖的多米诺骨牌式“级联”。 这种级联模型从全球体系的节点(“银行”)和边缘(“银行间敞口”)的结构和行为中推断出有关全球体系的结果。“渗流逻辑”是一种网络思维方式，它结合了凝聚态物理的直觉和概率，得出了级联的最终大小和影响的公式。这些公式适用于大型网络的极限，在较小的网络上与基于模拟的计算中观察到的统计结果给出了定量的一致。 该提案将加强和扩大该书中介绍的级联框架，主要目标有两个。首先，该项目将为新的随机级联模型家族模拟和开发分析方法，这些模型提取银行行为的基本方面，特别是两个或更多渠道的相互交织。由此得出的危机规模和影响公式，是了解加拿大银行体系等真实金融网络稳定性的数学实验室的基础。 第二个目标是研究监管约束下银行在非流动性资产市场中的战略行为。金融数学中的这个核心问题还与金融传染的贱卖渠道有关，在这种渠道中，压力过大的银行大规模出售固定资产，会导致价格螺旋式下降和系统范围的去杠杆化，而这是所有金融危机的关键。 研究最优银行策略将提高人们对流动性和银行行为应如何纳入系统性风险模型的级联机制的理解。级联模型的新分析方法将产生已被观察到在量化网络稳定性方面“不合理有效”的公式类型。这项研究将为金融从业者提供工具，例如测试加拿大法规变化对我们银行网络稳定性的影响。其他网络科学家将发现这些方法对于理解转折点和相变很有洞察力，特别是与加拿大社会的脆弱性相关的那些，如传染病的传播和电网的故障。

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.