AI 中文总结
研究推导詹森 - 香农散度和库尔贝克 - 莱布勒散度的统计特性与卡方基准值，通过检测信用违约概率分布变化展示其适用性，揭示两种散度在控制第一类错误和统计功效上的权衡，助从业者依需求选测度。
AI 中文摘要
散度测度是模型监测中检测分布变化的重要工具，在金融数据波动时尤为关键。虽然总体稳定性指数是最常用的测度，但詹森 - 香农散度和库尔贝克 - 莱布勒散度有独特优势。本研究扩展了Yurdakul和Naranjo（2020）的工作，一是推导了詹森 - 香农散度和库尔贝克 - 莱布勒散度的统计特性和卡方基准值；二是通过检测默顿、带跳跃的默顿以及带跳跃的随机波动率模型中信用违约概率的分布变化展示其适用性。结果表明这两种散度遵循卡方分布，存在重要实际权衡。詹森 - 香农散度在控制第一类错误方面表现出色，能使拒绝率接近5%，但在小样本时统计功效降低，从业者可据此根据优先事项选择测度。
英文摘要
Divergence measures are essential tools for detecting distributional shifts in model monitoring, particularly crucial given the volatility of financial data. While the Population Stability Index is the most widely used measure, Jensen-Shannon Divergence and Kullback-Leibler Divergence offer distinct advantages. Jensen-Shannon Divergence handles mixture models, addresses zero-binning problems, and is symmetric, while Kullback-Leibler Divergence excels in Bayesian model comparison. This study extends the work of Yurdakul and Naranjo (2020) with two primary contributions. First, we derive the statistical properties and chi-square benchmark values for Jensen-Shannon Divergence and Kullback-Leibler Divergence. Second, we demonstrate their applicability by detecting distributional changes in credit default probabilities from Merton, Merton with jump, and stochastic volatility with jump models. Our results establish that Jensen-Shannon Divergence and Kullback-Leibler Divergence follow chi-square distributions and reveal important practical trade-offs. Jensen-Shannon Divergence exhibits superior Type I error control, maintaining rejection rates closest to 5%, thereby minimizing false positives. However, this conservatism reduces statistical power at small samples (27% versus 32% for Population Stability Index and Kullback-Leibler Divergence at n = m = 200), requiring larger samples for reliable detection. This trade-off enables practitioners to select measures based on whether minimizing false alarms or maximizing detection sensitivity is the priority.
