发表机构
National Institute of Statistics and Applied Economics（国家统计与应用经济研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究量化2027年偿付能力监管标准II风险边际改革，通过归一化资本要求构建精确比率框架，证明机械降幅为20.83%-60.42%，并揭示资本时间结构的主导作用。
AI 中文摘要
2027年偿付能力监管标准II改革通过将规定的资本成本率从6%降至4.75%，并引入未来偿付能力资本要求的随时间衰减因子，重新校准了风险边际。本文开发了一个分析和数值框架，用以刻画最终监管校准的影响。通过将折现后的预计资本要求归一化为 runoff 时间上的概率分布，我们获得了修订后与先前风险边际之比的精确表示。该框架产生了严格的通用和特定期限界，通过随机占优刻画了较晚资本时间的影响，并表明当时间离散度变化时，平均 runoff 时间本身并不能决定改革效果。在给定平均 runoff 时间和期限的条件下，推导了额外的界。在给定预计SCR路径的条件下，机械性降低幅度介于20.83%和60.42%之间。对于成比例的最佳估计预测，精确的协方差分解识别了偏离比例性如何影响相对改革比率。在保持预计SCR路径固定的情况下，修订后的公式比先前校准具有更低的直接利率半弹性。一个简化形式的随机扩展进一步量化了由资本持续性不确定性引起的凸性效应。数值应用从已发布的精算 runoff 曲线重建风险边际计算，并通过受控的长期限、利率和持续性实验加以补充。结果表明，改革效果受未来资本的时间结构支配，并为评估预计资本曲线、风险边际简化和直接折现率敏感性提供了易处理的工具。
英文摘要
The 2027 Solvency II reform recalibrates the Risk Margin by reducing the prescribed cost-of-capital rate from 6% to 4.75% and introducing a time-dependent attenuation of future Solvency Capital Requirements. This paper develops an analytical and numerical framework for characterizing the effect of the final regulatory calibration. By normalizing discounted projected capital requirements into a probability distribution over run-off time, we obtain an exact representation of the ratio between the revised and previous Risk Margins. The framework yields sharp universal and horizon-specific bounds, characterizes the effect of later capital timing through stochastic dominance, and shows that mean run-off time alone does not determine the reform effect when temporal dispersion varies. Additional bounds are derived conditional on mean run-off time and horizon. Conditional on a given projected SCR path, the mechanical reduction lies between 20.83% and 60.42%. For proportional Best Estimate projections, an exact covariance decomposition identifies how departures from proportionality affect the relative reform ratio. Holding the projected SCR path fixed, the revised formula has a lower direct interest-rate semi-elasticity than the previous calibration. A reduced-form stochastic extension further quantifies convexity effects arising from uncertainty in capital persistence. Numerical applications reconstruct Risk Margin calculations from published actuarial run-off profiles and complement them with controlled long-horizon, interest-rate, and persistence experiments. The results show that the reform effect is governed by the temporal structure of future capital and provide tractable tools for assessing projected capital profiles, Risk Margin simplifications, and direct discount-rate sensitivity.
