arXiv:2512.12334q-fin.RMcs.LG2025-12

用动态贝叶斯网络改进市场风险的预期损失估算,尤其在压力情景下表现更优。

Extending the application of dynamic Bayesian networks in calculating market risk: Standard and stressed expected shortfall

  • 引入动态贝叶斯网络建模10天97.5%尾部风险,结合历史模拟与波动率模型。
  • 在正常分布下,EGARCH(1,1)对预期损失预测最准,GARCH(1,1)对压力预期损失最优。
  • 小样本下贝叶斯网络对尾部预测贡献有限,需优化其未来预测权重。

过去五年中,预期损失(ES)和压力预期损失(SES)已成为银行业监管的核心市场风险指标,尤其是在全球金融危机之后。因此,优化其估计方法至关重要。本文将动态贝叶斯网络(DBNs)的应用扩展至10天97.5%的预期损失与压力预期损失的估算,延续了之前对风险价值(VaR)的研究。以标普500指数作为美国银行股权交易部门的代理,我们比较了三种DBN结构学习算法与多种传统市场风险模型的表现,采用正态分布或偏斜学生t分布。回测显示,所有模型在2.5%水平上均未能产生统计上准确的ES与SES预测,反映出建模极端尾部行为的困难。对于ES,EGARCH(1,1)模型(正态分布)预测最准确;对于SES,GARCH(1,1)模型(正态分布)表现最佳。所有依赖分布的模型在使用偏斜学生t分布时性能显著下降。DBNs表现与历史模拟法相当,但其对尾部预测的贡献受限于其一日前瞻预测在收益分布中权重较小。未来研究应探索能增强前向型DBN预测对尾部风险估计影响的加权方案。

原文摘要 · Abstract (English)

In the last five years, expected shortfall (ES) and stressed ES (SES) have become key required regulatory measures of market risk in the banking sector, especially following events such as the global financial crisis. Thus, finding ways to optimize their estimation is of great importance. We extend the application of dynamic Bayesian networks (DBNs) to the estimation of 10-day 97.5% ES and stressed ES, building on prior work applying DBNs to value at risk. Using the S&P 500 index as a proxy for the equities trading desk of a US bank, we compare the performance of three DBN structure-learning algorithms with several traditional market risk models, using either the normal or the skewed Student's t return distributions. Backtesting shows that all models fail to produce statistically accurate ES and SES forecasts at the 2.5% level, reflecting the difficulty of modeling extreme tail behavior. For ES, the EGARCH(1,1) model (normal) produces the most accurate forecasts, while, for SES, the GARCH(1,1) model (normal) performs best. All distribution-dependent models deteriorate substantially when using the skewed Student's t distribution. The DBNs perform comparably to the historical simulation model, but their contribution to tail prediction is limited by the small weight assigned to their one-day-ahead forecasts within the return distribution. Future research should examine weighting schemes that enhance the influence of forward-looking DBN forecasts on tail risk estimation.

风险评估贝叶斯网络预期损失金融建模

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