Models of systemic risk in financial networks

自2007-08年金融危机以来，系统性风险（全球金融市场大规模甚至灾难性中断的风险）已成为全球研究的一个活跃领域。在这一丰富而复杂的学科中，危机预测是中心的、有争议的问题。我的研究始于2008年，总结在最近的一本书中[“传染！《金融网络中的系统性风险》是金融稳定领域的路线图。这本书模拟了一个银行网络中的危机，这个网络通过传递破坏性冲击的渠道相互连接，这些冲击可能发展成多米诺骨牌般的银行违约、银行储户挤兑和资产甩卖的“级联”。 这种级联模型给出了从节点（“银行”）和边缘（“银行间风险敞口”）的结构和行为推断出的关于全球系统的结果。 “逾渗逻辑”是一种网络思维，它结合了凝聚态物理学和概率的直觉，导致了级联的最终大小和影响的公式。这些公式在大型网络的限制下成立，在较小的网络上，与基于模拟的计算中观察到的统计结果定量一致。 该提案将加强和扩大本书中介绍的级联框架，主要有两个目标。首先，该项目将模拟和开发新的随机级联模型系列的分析方法，提取银行行为的基本方面，特别是两个或多个渠道的交织。由此产生的危机规模和影响的公式是数学实验室的基础，了解稳定的真实的金融网络，如加拿大银行系统。 第二个目标是研究银行在监管约束下的战略行为，即在非流动性资产市场中的行为。金融数学中的这个核心问题也与金融传染的火灾销售渠道有关，在这种渠道中，压力大的银行大规模出售其固定资产，造成价格螺旋式下降和系统范围的去杠杆化，这是所有金融危机的关键。 研究最佳银行战略将有助于理解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。 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人员提供工具，例如测试加拿大法规变化对我们银行网络稳定性的影响。 其他网络科学家会发现这些方法对于理解临界点和相变很有见地，特别是那些与加拿大社会的脆弱性有关的问题，如传染病的传播和电网的崩溃。

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.