NatPar: Natural Parametric Modeling

2026-08-25

AI Summary

本文提出自然参数化保险模型NatPar，通过将参数指数合同化来解决自然灾害建模问题，并通过案例研究展示了其在时间维度上的支付特性。

Abstract

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.

Problem

• Natural Parametric Insurance
• Risk Allocation
• Basis Risk
• Tail Dependence
• Annual Average Loss

Innovation

• Natural Parametric (NatPar)
• Basis-Exceedance Diagnostics (BEP+/-)
• Tail Risk Allocation