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使用非线性SPDE模型分析系统性违约传染

文章 arXiv papers · 作者: Ben Hambly et al.
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总结

这项研究为大型金融系统构建动态平均场系统性风险模型。每家机构的违约距离以扩散过程表示，零点为吸收边界。模型包含代表共同风险敞口或羊群效应的共同噪声、漂移中的均值回归，以及内生传染机制：一家机构违约可能缩短其他机构的违约距离。

系统的极限行为由正半轴上的非线性随机偏微分方程刻画，并在零点设有边界条件。其密度描述相应扩散过程的条件分布，作者还给出了分析中使用的热核型上界。在某些共同噪声实现和均值回归速率下，模型可能产生边界质量损失的快速增加，对应违约聚集。摘录介绍的是数学模型和理论结果；没有报告实证校准、对危机数据的验证或交易应用。

核心观点

  • 机构的违约距离被建模为在零点吸收的扩散过程。
  • 共同噪声和均值回归用于表示共同风险与漂移动态。
  • 内生传染机制使一家机构违约后，其他机构的违约距离也可能缩短。
  • 非线性SPDE刻画平均场极限及其条件密度。
  • 某些模型条件会使边界概率质量快速流失，从而加速违约聚集。

标签

风险管理统计学
全文
# An SPDE Model for Systemic Risk with Endogenous Contagion


# An SPDE Model for Systemic Risk with Endogenous Contagion









We propose a dynamic mean field model for `systemic risk' in large financial systems, which we derive from a system of interacting diffusions on the positive half-line with an absorbing boundary at the origin. These diffusions represent the distances-to-default of financial institutions and absorption at zero corresponds to default. As a way of modelling correlated exposures and herd behaviour, we consider a common source of noise and a form of mean-reversion in the drift. Moreover, we introduce an endogenous contagion mechanism whereby the default of one institution can cause a drop in the distances-to-default of the other institutions. In this way, we aim to capture key `system-wide' effects on risk. The resulting mean field limit is characterized uniquely by a nonlinear SPDE on the half-line with a Dirichlet boundary condition. The density of this SPDE gives the conditional law of a non-standard `conditional' McKean--Vlasov diffusion, for which we provide a novel upper Dirichlet heat kernel type estimate that is essential to the proofs. Depending on the realizations of the common noise and the rate of mean reversion, the SPDE can exhibit rapid accelerations in the loss of mass at the boundary. In other words, the contagion mechanism can give rise to periods of significant systemic default clustering.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。