标题： 关于相关性压力测试的笔记 显示英文标题

标题： Notes on Correlation Stress Tests

摘要： 本文档概述了在金融风险管理背景下，对金融时间序列协方差的压力测试方法。它讨论了协方差矩阵之间的测地线距离如何暗示协方差压力测试的合理性概念。在此方法中，相关性压力测试跨越了协方差矩阵Fisher-Rao流形中常确定值的子流行。提出了一种简洁且几何不变的相关性压力测试的任意大规模定义，并讨论了一些例子。 显示英文摘要

摘要： This note outlines an approach to stress testing of covariance of financial time series, in the context of financial risk management. It discusses how the geodesic distance between covariance matrices implies a notion of plausibility of covariance stress tests. In this approach, correlation stress tests span a submanifold of constant determinant of the Fisher--Rao manifold of covariance matrices. A parsimonious geometrically invariant definition of arbitrarily large correlation stress tests is proposed, and a few examples are discussed.