NatPar：自然参数化建模
NatPar: Natural Parametric Modeling
AI总结：
该研究提出 NatPar 保险，基于 NatCat 建模机制，用合同化参数指数替代损失赔偿，通过霜冻案例揭示其尾部风险分配规律，为保险行业提供实用标准。
AI中文摘要：
我们开发了自然参数化（NatPar）保险，作为自然巨灾（NatCat）建模的自然延伸：采用相同的危险-风险暴露-脆弱性-金融机制，用一份合同化的参数指数替代 indemnity（ indemnity 指实际损失赔偿）损失调整。我们的目标是实用的——一种受巨灾保险行业现有运作方式启发的标准方法，而非另一种最优合同准则。这带来两项收益：其一，它确定了报告的制定方式：NatPar 合同以原生 NatCat 语言（年平均损失、EP/AEP/OEP 曲线、重现期水平）报告，同时补充双向基差超限诊断（BEP+/-），并将其提升至 EP 曲线对损失所具有的核心地位——即基差风险的规范分布视角，而非补充数字；其二，同一标准展示了尾部如何在被保险人和保险人之间重新分配。霜冻案例研究得出核心结果：关键在于时间，而非平均值。在保持合同 AAL（年平均损失）中性的情况下，有界赔付无法跟随无界的风险暴露尾部，因此均值均等化会区分不同重现期下的超付与欠付：被保险人在短时间范围内获益，而保险人在数十年的交叉点后摆脱深层尾部。这逆转了尾部依赖的影响——当区域联合达到极端时，有界赔付会累积，保险人则重新吸收深层尾部。
英文摘要：
We develop natural parametric (NatPar) insurance as the natural next step from natural-catastrophe (NatCat) modelling: the same hazard-exposure-vulnerability-finance machinery, with a parametric index made contractual in place of indemnity loss adjustment. Our aim is practical - a standard approach inspired by how the catastrophe-insurance industry already operates, not another optimal-contract criterion. This delivers two payoffs. First, it fixes how reporting is formulated: NatPar contracts are reported in the native NatCat language (annual average loss, EP/AEP/OEP curves, return-period levels), complemented with two-sided basis-exceedance diagnostics (BEP+/-) elevated to the central status the EP curve holds for losses - the canonical distributional view of basis risk, not a supplementary number. Second, the same standard shows how the tail is reallocated between insuree and insurer. A frost case study yields the central result: it is about time, not average. Holding a contract AAL-neutral, the bounded payout cannot follow the unbounded exposure tail, so equalising the mean separates over- and under-payment across return periods: the insuree gains at short horizons while the insurer sheds the deep tail past a crossover of several decades. This reverses under tail dependence - when regions reach extremes jointly, bounded payouts stack and the insurer reabsorbs the deep tail.
