英文标题：
《Sensitivity of the Eisenberg-Noe clearing vector to individual interbank
liabilities》
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作者：
Zachary Feinstein, Weijie Pang, Birgit Rudloff, Eric Schaanning,
Stephan Sturm, Mackenzie Wildman
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最新提交年份：
2018
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英文摘要：
We quantify the sensitivity of the Eisenberg-Noe clearing vector to estimation errors in the bilateral liabilities of a financial system in a stylized setting. The interbank liabilities matrix is a crucial input to the computation of the clearing vector. However, in practice central bankers and regulators must often estimate this matrix because complete information on bilateral liabilities is rarely available. As a result, the clearing vector may suffer from estimation errors in the liabilities matrix. We quantify the clearing vector\'s sensitivity to such estimation errors and show that its directional derivatives are, like the clearing vector itself, solutions of fixed point equations. We describe estimation errors utilizing a basis for the space of matrices representing permissible perturbations and derive analytical solutions to the maximal deviations of the Eisenberg-Noe clearing vector. This allows us to compute upper bounds for the worst case perturbations of the clearing vector in our simple setting. Moreover, we quantify the probability of observing clearing vector deviations of a certain magnitude, for uniformly or normally distributed errors in the relative liability matrix. Applying our methodology to a dataset of European banks, we find that perturbations to the relative liabilities can result in economically sizeable differences that could lead to an underestimation of the risk of contagion. Our results are a first step towards allowing regulators to quantify errors in their simulations.
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中文摘要：
我们量化了艾森伯格-诺伊清算向量对程式化环境下金融系统双边负债估计误差的敏感性。银行间负债矩阵是计算清算向量的关键输入。然而，在实践中，央行行长和监管者必须经常估计该矩阵，因为很少有关于双边债务的完整信息。因此，清算向量可能会在负债矩阵中出现估计错误。我们量化了清除向量对此类估计误差的敏感性，并表明其方向导数与清除向量本身一样，是不动点方程的解。我们利用表示允许扰动的矩阵空间的基来描述估计误差，并导出艾森伯格-诺埃清除向量最大偏差的解析解。这允许我们在简单设置中计算清除向量最坏情况下扰动的上界。此外，对于相对责任矩阵中的均匀或正态分布误差，我们量化了观察到一定量级的清除向量偏差的概率。将我们的方法应用于欧洲银行的数据集，我们发现，相对负债的扰动可能会导致经济上的巨大差异，从而导致对传染风险的低估。我们的结果是朝着允许监管机构量化模拟误差迈出的第一步。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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