重叠时间窗口下评级系统长期校准的假设检验
A hypothesis test for the long-term calibration in rating systems with overlapping time windows
AI总结：
提出一种统计检验方法，验证评级系统中重叠时间窗口的长期校准监管要求，处理未知方差并推广至组合层面，分析持续客户和参考日期客户数量的影响。
摘要：
我们提出了一种统计检验，可用于验证关于评级系统中重叠时间窗口的长期校准的监管要求。第一步，我们证明长期违约率在违约实现的随机效应下近似服从正态分布。然后，我们对重叠时间窗口引起的相关效应进行了详细分析，并解决了长期违约率中违约概率分布未知的问题。在此背景下，我们提出了几种保守校准检验方法，这些方法能够处理检验统计量中的未知方差。我们提出了针对单个评级等级的检验，然后通过适当调整检验统计量将其推广到组合层面。最后，我们进行了比较静态分析，研究了持续客户和每个参考日期客户数量的影响。
英文摘要：
We present a statistical test that can be used to verify supervisory requirements concerning overlapping time windows for the long-term calibration in rating systems. In a first step, we show that the long-run default rate is approximately normally distributed with respect to random effects in default realization. We then perform a detailed analysis of the correlation effects caused by the overlapping time windows and solve the problem of an unknown distribution of default probabilities for the long-run default rate. In this context, we present several methods for a conservative calibration test that can deal with the unknown variance in the test statistic. We present a test for individual rating grades, and then pass to the portfolio level by suitably adapting the test statistic. We conclude with comparative statics analysing the effect of persisting customers and the number of customers per reference date.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
