Large-loss pricing for excess layers
Losses above a threshold are fitted with a generalised Pareto distribution to price excess-of-loss reinsurance layers, with the threshold choice and its effect on the layer price shown.
GRA · Insurance Nexus
空间金融资本与危害、风险暴露和转型的交汇之处
面向保险尾部的极值理论
Extreme value theory gives the tail of the loss distribution its shape: how large a rare event loss may be, how losses accumulate in a bad year, and how uncertain those estimates become beyond the record. Capital, reinsurance and catastrophe pricing all rest on it.
01目录
Extreme value theory for insurance tails in five parts.
02申请
What extreme value theory and tail risk does here.
Extreme value theory and 尾部风险 study the behaviour of rare, high-impact events. They provide methods to estimate the magnitude and frequency of extremes beyond the range of observed data. In insurance and catastrophe, climate and hazards and health and biosecurity, extreme value methods set design levels and capital buffers for rare events. Tail dependence analysis reveals when extremes in different 系统 tend to occur together. The canonical description is on STEM Commons.
Tail measures for solvency capital
Loss distributions are extended into the tail to estimate 风险价值 and tail value at risk at regulatory confidence levels, with parameter uncertainty and alternative fits reported.
Tail dependence across lines and perils
Copulas and multivariate extreme value models examine whether extreme losses in different lines, regions or asset classes tend to occur together, which governs how much diversification credit is defensible.
03空间金融
风险暴露、危害与超越概率曲线。
哪些地方在严重年份造成损失，以及损失向再保险蔓延的程度。示意性设计数值。
04数据
该方法使用的输入。
Datasets and records used by extreme value theory and 尾部风险 on this platform, with the role each plays and the label its values carry. Sources are listed in 来源登记册.
| 数据 | 角色 | 标签 |
|---|---|---|
| Large-loss histories | Tail fitting | 观测 |
| Industry catastrophe loss records | Event severity | 估算 |
| 巨灾模型 event sets | Synthetic tail extension | 模型估算 |
| Hazard maxima such as wind speed and rainfall | Hazard tail behaviour | 观测 |
05监测
Tail fit.
团队遵循该方法时会使用的界面：其指标、状态与决策。名称为示例，数值仅作示意。
Tail fit
Insurance · Extreme value theory for insurance · Run R-7661
Shape parameter uncertainGRA · Insurance Nexus
Return level curve
方法卡
- 方法
- 极值理论与尾部风险
- 方法
- peaks over threshold
- Threshold
- 90th percentile
- 标签
- 模型估算
参数
generalised Pareto fit
| Shape ξ | 0.22 | −0.03 | 0.45 | heavy tail if above zero |
| Scale σ | 2.7 | 1.0 | 6.9 | units of the variable |
| Exceedances | 88 | declustered |
06验证
结果如何核查。
Fits are checked with diagnostic plots, goodness-of-fit tests and out-of-sample comparison. Sensitivity to threshold and record length is reported.
| 核查 | 如何开展 |
|---|---|
| Threshold stability | Tail parameters are estimated across a range of thresholds and the choice is justified by stability plots |
| Goodness of fit in the tail | Fits are judged on tail behaviour, not overall fit, using quantile plots and out-of-sample large losses |
| Parameter uncertainty | Confidence intervals for return-period losses are reported, by bootstrap or profile likelihood |
| Indexation and stationarity | Losses are brought to a common basis for inflation and exposure, and trends are tested before fitting |
Extrapolation far beyond the data is highly uncertain. Changing climates and markets violate stationarity assumptions.
07损失模型
损失超越、年均损失和可能最大损失。
处于覆盖范围内的投资组合每年预期损失，以及保险公司和贷款机构定价所依据的 1/100 和 1/250 水平下的预期损失，均来自每个 巨灾模型 uses. Teaching model with stated illustrative values, not a prediction. The map on this page shows The Gulf of Mexico coast; the model itself is not tied to a place.
控制措施
- 典型年度危害强度（所在地）
- 1.00 强度指数
- 极端值的扩散（尺度）
- 强度指数 0.80
- 损失一半价值时的强度
- 4.00 强度指数
- 脆弱性的离散程度
- 0.55
- 危害足迹中的价值占比
- 40%
- 防护标准（重现期）
- 50 年
读数
- 年均损失
- 占价值的 0.51%
- 百年一遇（1/100）的损失
- 占价值的 24.5%
- 250 年一遇（1/250）的损失
- 占价值的 28.4%
- 百年一遇（1/100）的强度
- 强度指数 4.68
数字、方法与来源
| 重现期（年） | 强度（强度指数） | 损失（占价值的 %） |
|---|---|---|
| 1 | 0.09 | 0.00 |
| 2 | 1.27 | 0.00 |
| 4 | 1.91 | 0.00 |
| 7 | 2.47 | 0.00 |
| 13 | 3.00 | 0.00 |
| 24 | 3.51 | 0.00 |
| 44 | 4.02 | 0.00 |
| 82 | 4.53 | 23.55 |
| 154 | 5.03 | 26.44 |
| 287 | 5.53 | 28.87 |
| 536 | 6.03 | 30.88 |
| 1,000 | 6.53 | 32.53 |
方法
- Gumbel 极值危害 Gumbel (1958), Statistics of Extremes, Columbia University Press
- 对数正态易损性（脆弱性） FEMA (2003), HAZUS-MH Technical Manual
- 超越概率曲线与年均损失 Grossi and Kunreuther (2005), Catastrophe Modeling, Springer
- 堤防效应 Di Baldassarre and others (2013), Socio-hydrology, HESS 17
- 不确定性扇形图（参数蒙特卡罗） Spiegelhalter, Pearson and Short (2011), Visualising uncertainty about the future, Science 333
- 单因素敏感性（龙卷风图） Saltelli and others (2008), Global Sensitivity Analysis: The Primer, Wiley
数据
The model runs on the teaching values set by the controls. To calibrate it for a place, read it against these admitted layers and series, which this page’s map can draw:
- 河流 Natural Earth
- 城市范围 Natural Earth
- 城市 Natural Earth
- 过去一周 M4.5+ 地震（USGS） 美国地质调查局 · 登记 usgs.earthquake.summary-feeds
- 降雨率，最近半小时（IMERG） NASA GPM IMERG Early · 登记 nasa.gibs.context-live-layers
- 河流流量预报，30 天及范围（GloFAS via Open-Meteo） Open-Meteo.com（CC BY 4.0）、Copernicus GloFAS · 登记 open-meteo.public-pages
- 建成区与居民点范围，2010 年（HBASE，Landsat） CIESIN/Columbia、NASA SEDAC HBASE · 登记 sedac.context-urban-layers
贯穿六大支柱，由 Nexus Consortium 牵头
09孪生与级联模拟器
Trace a shock in extreme value theory for insurance tails to the balance sheet.
Assembled from the Nexus Standards area profile 保险与再保险: the shocks it names, the 系统 and sectors that carry the loss, the controls that dampen it and the data that observe it. Pick an initiating shock and step through the cascade to see which exposures it reaches and where losses could concentrate. The Map view places the run on an example geography with open data. Every weight is a stated assumption. An exercise, not a forecast, a valuation, a rating or investment advice. To model a place of your own choosing, open the full System Builder.
灾害
- 热带气旋
- 地震
- 冰塞洪水
- 野火
- Storm surge （在下游引发）
- Intense rainfall （在下游引发）
- 河流洪水（在下游引发）
- Flash flood (set off downstream)
- 危险海浪（在下游引发）
- 大范围停电（在下游引发）
- 大规模流离失所（在下游引发）
- 沿海洪水（在下游引发）
- Aftershock sequence (set off downstream)
- Fault surface rupture (set off downstream)
- Soil liquefaction (set off downstream)
- Slope slide (set off downstream)
- Rockfall (set off downstream)
- Tsunami (set off downstream)
控制措施
NS-0章程与原则NS-3风险记录 UNI（语法、旧编码对照、分配机构）NS-9情境 UNI（部署、实例、计划实例）NS-10政策和条款（机器可读的义务：定义、约束、评估和执行）NS-11验证与监测（证据、证明、零信任符合性观测）NS-14符合性及与外部标准的对照NRS-F3保险、巨灾风险与保护缺口NRS-H113危害类别：金融体系脆弱性（NHS-1 soc.financial-system）NRS-U17宇宙 platform profile: Insurance NexusNRS-H71危害类别：深时与宇宙灾难（NHS-1 planet.deep-time）NRS-H65危害类别：超越行星边界（NHS-1 planet.boundary）NRS-F8参数化与指数型风险转移
观测
- OECD Data Explorer (incl. Creditor Reporting System, insurance and pension statistics) (listed for reference)
- Insurance statistics (listed for reference)
- USGS earthquake GeoJSON summary feeds (listed for reference)
- Direct economic loss attributed to disasters in relation to global gross domestic product (GDP)
- Direct economic loss attributed to disasters in relation to global gross domestic product
- (a) Number of commercial bank branches per 100,000 adults and (b) number of automated teller machines (ATMs) per 100,000 adults
示例地理范围
- 西欧：152 个六边形网格
- 过去半小时降雨率（IMERG），NASA GIBS
- 今夜夜间灯光与停电（VIIRS 昼夜波段），NASA GIBS
- 穿透云层的地表水，30 m（OPERA DSWx-S1 雷达），NASA GIBS
- Carbon monoxide, smoke transport (AIRS), NASA GIBS
11风险暴露、损失与资本
What extreme value theory for insurance tails means for exposure, loss and capital.
风险官、监管者或财政部会要求的风险暴露、损失、情景和资本视图，以及它们据以报告的框架。结构遵循监管和精算实务。数值为说明性：绝非价格、评级或建议。
各重现期的风险暴露与损失
How losses from extreme value theory for insurance tails grow with severity, gross and net of reinsurance, against capital.
| 重现期 | 年概率 | 总损失 | 净损失 | 净额，资本 = 100 |
|---|---|---|---|---|
| 1/10（10 年一遇） | 0.10 | 14 | 10 | 10 |
| 1/50（50 年一遇） | 0.02 | 33 | 21 | 21 |
| 1/100（100 年一遇） | 0.01 | 46 | 27 | 27 |
| 1/250（250 年一遇） | 0.004 | 68 | 39 | 39 |
| 年均损失 | 3.1 | 2.2 | 2.2 |
NGFS 气候情景 · 央行与监管机构绿色金融网络IFRS S2 气候相关披露 · ISSBTCFD 建议 · 金融稳定理事会 TCFD有效管理气候相关金融风险的原则 · 巴塞尔银行监管委员会
12已关联
本页在整个联合体中通向何处。
13问题
问题与解答。
What are the limits of extreme value theory and tail risk in this field?
Extrapolation far beyond the data is highly uncertain. Changing climates and markets violate stationarity assumptions.
结果如何核查？
Fits are checked with diagnostic plots, goodness-of-fit tests and out-of-sample comparison. Sensitivity to threshold and record length is reported.
本页面上的数值是真实的吗？
The data names, roles and checks are real descriptions of practice. The canvas shows a design of the method’s use, not a run; no result is reported here.
该方法还应用于何处？
维持社会运转的各个 规范方法页面 列出应用该方法的每个平台。
报告贡献
从本页贡献证据。
报告 is the Consortium’s quarterly publication. What you know about this subject can become evidence, a case or a correction in the next edition, credited to you and published under CC BY 4.0 where it is your own work.
全球风险联盟（Global Risks Alliance）Insurance Nexus金融与保险准备度全球部门风险与韧性
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