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GRA · Reinsurance and Catastrophe

Spatial financeWhere capital meets hazard, exposure and transition

Extreme value theory and tail risk for reinsurance and catastrophe

Extreme value theory describes the tail of loss and hazard distributions: how large rare events may be and how uncertain those estimates become beyond the record. In reinsurance it underpins excess layer pricing, return period losses and the tail of catastrophe models.

پرسیارێک بنێرە Back to STEM foundation of Reinsurance and Catastrophe
01ناوەڕۆک

Extreme value theory and tail risk for reinsurance and catastrophe in five parts.

پرۆتۆکۆل5 steps
  1. 01بەکارهێنانWhat extreme value theory and tail risk does here
  2. 02داتاWhat the method consumes
  3. 03پشتڕاستکردنەوەHow results are checked
  4. 04ConnectionsTopics that rely on this method
  5. 05StewardshipWho maintains the method
02بەکارهێنان

What extreme value theory and tail risk does here.

Extreme value theory and tail risk 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 disaster and crisis, extreme value methods set design levels and capital buffers for rare events. Tail dependence analysis reveals when extremes in different سیستەمەکان tend to occur together. The canonical description is on the STEM Commons.

Pricing high excess layers

Losses above a threshold are fitted with a generalised Pareto distribution to price upper layers, with the threshold choice and its effect shown.

Hazard return levels

Annual maxima of wind speed, rainfall or surge are fitted to estimate return levels, with confidence intervals reported.

Tail dependence between perils

Joint extremes of perils or regions are examined to judge how much diversification credit is defensible.

03Spatial finance

Exposure, hazard and the exceedance curve.

Which places drive loss in a severe year, and how far it reaches into reinsurance. Illustrative design values.

Coastal exposure under cyclone and earthquake zones, beside the loss curve it produces.Illustrative design values, not a model output or a price.
04داتا

What the method consumes.

Datasets and records used by extreme value theory and tail risk on this platform, with the role each plays and the label its values carry. Sources are listed in the source register.

داتاڕۆڵناونیشان
Large-loss historiesTail fittingچاودێریکراو
Hazard maxima recordsHazard tailsچاودێریکراو
مۆدێلی کارەسات event setsSynthetic tailsمۆدێلکراو
05چاودێری

Tail fit.

The screen a team would use to follow this method: its measures, states and decisions. Names are examples and values are illustrative.

Tail fit

Reinsurance and catastrophe · Extreme value theory and tail risk · Run R-8449

Shape parameter uncertainGRA · Reinsurance and Catastrophe

Return level curve

Method card

ڕێگا
تیۆری بەهای زۆرداری و مەترسیی کلک
ڕێباز
peaks over threshold
Threshold
90th percentile
ناونیشان
مۆدێلکراو

Parameters

generalised Pareto fit

Shape ξ0.19−0.030.48heavy tail if above zero
Scale σ2.21.07.0units of the variable
Exceedances41declustered
Tail fit: the screen’s structure, terms and states for Reinsurance and catastrophe.ناو و بەهای نموونەیی؛ دیزاینێکە، نەک تۆمار یان سیستەمی ڕاستەوخۆ.
06پشتڕاستکردنەوە

How results are checked.

Fits are checked with diagnostic plots, goodness-of-fit tests and out-of-sample comparison. Sensitivity to threshold and record length is reported.

بپشکنەHow it is done
Threshold stabilityTail parameters are checked across thresholds
Parameter uncertaintyConfidence intervals for return levels are reported
StationarityTrends are tested before fitting

Extrapolation far beyond the data is highly uncertain. Changing climates and markets violate stationarity assumptions.

07Loss model

Loss exceedance, average annual loss and probable maximum loss.

The loss a portfolio in the footprint can expect per year and at the 1 in 100 and 1 in 250 levels that insurers and lenders price, from the same three blocks every catastrophe model 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.

کۆنترۆڵەکان

Typical annual hazard intensity (location)
1.00 intensity index
بڵاوبوونەوەی لێکەوتە توندەکان (پێوەر)
0.80 intensity index
توندییەک کە تێیدا نیوەی بەها لەدەست دەچێت
4.00 intensity index
بڵاوبوونەوەی لاوازی
0.55
بەشی بەها لە شوێنپێی مەترسیدەردا
40%
ستانداردی پاراستن (ماوەی گەڕانەوە)
50 ساڵ

خوێندنەوەکان

تێکڕای زیانی ساڵانە
0.51% of value
زیان لە 1 لە 100 ساڵدا
24.5% of value
زیان لە 1 لە 250 ساڵدا
28.4% of value
توندی لە 1 لە 100 ساڵدا
4.68 intensity index
ژمارە، ڕێگا و سەرچاوەکان
ماوەی گەڕانەوە (ساڵ)Intensity (intensity index)زیان (% ی بەها)
10.090.00
21.270.00
41.910.00
72.470.00
133.000.00
243.510.00
444.020.00
824.5323.55
1545.0326.44
2875.5328.87
5366.0330.88
1,0006.5332.53

ڕێگاکان

  1. مەترسیدەری بەهای زۆرداری Gumbel Gumbel (1958)، Statistics of Extremes، Columbia University Press
  2. ناسکیی لۆگنۆرماڵ (لاوازی) FEMA (2003)، HAZUS-MH Technical Manual
  3. چەمکی ئەگەری تێپەڕبوون و تێکڕای زیانی ساڵانە Grossi و Kunreuther (2005)، Catastrophe Modeling، Springer
  4. کاریگەری بەربەست Di Baldassarre و ئەوانی دیکە (2013)، Socio-hydrology، HESS 17
  5. پەنجەی نادڵنیایی (مۆنتی کارلۆی پارامیتەر) Spiegelhalter, Pearson و Short (2011)، Visualising uncertainty about the future، Science 333
  6. هەستیاریی یەک-یەک (تۆرناد) Saltelli و ئەوانی دیکە (2008)، Global Sensitivity Analysis: The Primer، Wiley

داتا

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:

  • ڕووبارەکان Natural Earth
  • بەرینی شارەکان Natural Earth
  • شارەکان Natural Earth
  • بوومەلەرزەکانی M4.5+، هەفتەی ڕابردوو (USGS) U.S. Geological Survey · register usgs.earthquake.summary-feeds
  • ڕێژەی باران، نیو کاتژمێری ڕابردوو (IMERG) NASA GPM IMERG Early · register nasa.gibs.context-live-layers
  • پێشبینی ڕۆیشتنی ڕووبار، 30 ڕۆژ لەگەڵ مەودا (GloFAS لە ڕێگەی Open-Meteo) Open-Meteo.com (CC BY 4.0), Copernicus GloFAS · register open-meteo.public-pages
  • بەرینی دروستکراو و نیشتەجێبوون، 2010 (HBASE، Landsat) CIESIN/Columbia, NASA SEDAC HBASE · register sedac.context-urban-layers
Loss exceedance, average annual loss and probable maximum loss. Illustrative teaching model: it runs on the values set by the controls, not on measured data. Methods: Gumbel extreme-value hazard (Gumbel (1958), Statistics of Extremes, Columbia University Press); Lognormal fragility (vulnerability) (FEMA (2003), HAZUS-MH Technical Manual); Exceedance-probability curve and average annual loss (Grossi and Kunreuther (2005), Catastrophe Modeling, Springer).

لە ناو شەش کۆڵەکەکەدا، بە سەرپەرشتیی Nexus Consortium

08Connections

Topics that rely on this method.

09شبیهسازی دووانە و زنجیرەیی

Trace a shock to the balance sheet.

Assembled from the Nexus Standards area profile بیمە و دووبارەبیمە: the shocks it names, the سیستەمەکان 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.

مەترسیدەرەکان

  • Tropical cyclone
  • بوومەلەرزە
  • Ice-jam flood
  • ئاگری دارستان
  • Storm surge (set off downstream)
  • Intense rainfall (set off downstream)
  • River flood (set off downstream)
  • Flash flood (set off downstream)
  • Dangerous surf (set off downstream)
  • پچڕانی کارەبای فراوان (لە خوارەوە دەستپێدەکات)
  • ئاوارەبوونی بەکۆمەڵ (لە خوارەوە دەستپێدەکات)
  • Coastal flood (set off downstream)
  • 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)

کۆنترۆڵەکان

  • NS-0 دەستوور و بنەماکان
  • NS-3 UNIەکانی تۆماری مەترسی (ڕێزمان، خشتەی گواستنەوەی کۆن، دەسەڵاتی تەرخانکردن)
  • NS-9 UNIی ناوەڕۆکی (دامەزراندنەکان، نموونەکان، نموونەکانی پڕۆگرام)
  • NS-10 Policies and clauses (machine-readable obligations: definition, binding, evaluation and enforcement)
  • NS-11 سەلماندن و چاودێری (بەڵگە، گواهییەکان، چاودێریی گونجان لەگەڵ zero-trust)
  • NS-14 پابەندبوون و هاوتاکردن لەگەڵ ستانداردی دەرەکی
  • NRS-F3 بیمە، مەترسیی کارەسات و کەلێنەکانی پاراستن
  • NRS-H113 خێزانی مەترسیدەر: ناسکیی سیستەمی دارایی (NHS-1 soc.financial-system)
  • NRS-U17 Universe platform profile: Insurance Nexus
  • NRS-H71 خێزانی مەترسیدەر: کارەساتە کەونی و کاتی قووڵەکان (NHS-1 planet.deep-time)
  • NRS-H65 خێزانی مەترسیدەر: پێشێلکردنی سنوورەکانی گۆی زەوی (NHS-1 planet.boundary)
  • NRS-F8 گواستنەوەی مەترسیی پارامێتری و لەسەر بنەمای نیشاندەر

چاودێری

  • 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

جوگرافیای نموونە

  • Western Europe: 152 hexagonal cells
  • ڕێژەی بارین، نیو کاتژمێری ڕابردوو (IMERG)، NASA GIBS
  • ڕووناکییەکانی شەو ئەمشەو، پچڕانی کارەبا (VIIRS Day/Night Band)، NASA GIBS
  • ئاوی ڕووی زەوی لە ڕێگەی هەورەوە، 30 م (ڕادارەی OPERA DSWx-S1)، NASA GIBS
  • Carbon monoxide, smoke transport (AIRS), NASA GIBS
10Stewardship

Who maintains the method.

Reinsurance and Catastrophe stewards extreme value theory and tail risk for the Consortium and reviews how it is applied across platforms.

Canonical page: Extreme value theory and tail risk

11Exposure, loss and capital

What it means for exposure, loss and capital.

The exposure, loss, scenario and capital views a risk officer, supervisor or ministry of finance would ask for, with the frameworks they report against. Structures follow supervisory and actuarial practice. Values are illustrative: never prices, ratings or advice.

Exposure and loss at return periods

How losses from extreme value theory and tail risk for reinsurance and catastrophe grow with severity, gross and net of reinsurance, against capital.

1 in 101 in 501 in 1001 in 250grossnet of reinsurance800
Return periodAnnual probabilityGross lossNet lossNet, capital = 100
1 in 100.10141010
1 in 500.02332121
1 in 1000.01462727
1 in 2500.004683939
تێکڕای زیانی ساڵانە3.12.22.2
Illustrative loss index for a example portfolio (capital = 100): the exceedance-probability form insurers and supervisors read. Not data on any institution, not a price or a rating.
NGFS climate scenarios · Network for Greening the Financial SystemIFRS S2 Climate-related Disclosures · ISSBTCFD recommendations · Financial Stability Board TCFDPrinciples for the effective management of climate-related financial risks · Basel Committee on Banking Supervision
12پرسیارەکان

پرسیار و وەڵام.

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.
How are results checked?
Fits are checked with diagnostic plots, goodness-of-fit tests and out-of-sample comparison. Sensitivity to threshold and record length is reported.
Are the values on this page real?
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.
Where else is this method applied?
ئەو canonical method page lists every platform that applies it.
Reportsبەشداربە

لەم لاپەڕەیەوە بەڵگە پێشکەش بکە.

Reports 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.

Global Risks Allianceبیمەی ئەتکایی و کارەساتئامادەیی دارایی و بیمەڕێگا و تەکنیکی

هەرگیز داتای کەسی، وردەکاریی هەستیاری ژێرخان یان هیچ شتێک مەنێرە کە مافی بڵاوکردنەوەت نییە. بەشدارییەک پێش بەکارهێنان پێداچوونەوەی بۆ دەکرێت؛ ناردنی ماف نابەخشێت بە نووسەرایەتی یان بەڕێوەبردنی ڕاگەیاندن، و پاڵپشتی دارایی هەرگیز دۆزینەوەیەک ناکڕێت.

بیمەی ئەتکایی و کارەسات

Bring an exposure or capital question to the Alliance.

زانیاری و پرسیار ئەمڕۆ کراوەن. پرسیارێک ژمارەی ئاماژەی پێدەدرێت و هەنگاوی دواتر دیاری دەکات؛ داواکاری، پارەدان، تەرخانکردنی کۆمپیوتەر و تۆمارکردن تەنیا کاتێک دەکرێنەوە کە تیم، مەرج و توانای پێداچوونەوەیان هەبێت.

Propose a readiness pilot بینینی هەموو ڕێگاکانی پەیوەندی
یاسایی

نەخشە، داتا و وێنەکانی ئەم ماڵپەڕە بۆ ناوەڕۆک و زانیاریی گشتی پیشان دراون. ئامۆژگاری، پێشبینی یان ئاگادارکردنەوە نین؛ سنوورەکانی زانیارییەکە لە ڕەتکردنەوەی بەرپرسیارێتی و ئاگاداریی داتادا دەستنیشان کراون.