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
Spatial financeWhere capital meets hazard, exposure and transition
Extreme value theory for insurance tails
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.
01Naverok
Extreme value theory for insurance tails in five parts.
02Serlêdan
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 health and biosecurity, extreme value methods set design levels and capital buffers for rare events. Tail dependence analysis reveals when extremes in different pergalan tend to occur together. The canonical description is on the STEM Commons.
Tail measures for solvency capital
Loss distributions are extended into the tail to estimate value at risk 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.
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.
04Dane
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.
| Dane | Rol | Nîşan |
|---|---|---|
| Large-loss histories | Tail fitting | ÇAVDÊRÎKIRÎ |
| Industry catastrophe loss records | Event severity | TEXMÎNKIRÎ |
| Modela karesatê event sets | Synthetic tail extension | MODELKIRÎ |
| Hazard maxima such as wind speed and rainfall | Hazard tail behaviour | ÇAVDÊRÎKIRÎ |
05Çavdêrî bike
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
Insurance · Extreme value theory for insurance · Run R-7661
Shape parameter uncertainGRA · Insurance Nexus
Return level curve
Method card
- Rêbaz
- Teoriya nirxên tund û xetera dûvê
- Nêzîkatî
- peaks over threshold
- Threshold
- 90th percentile
- Nîşan
- MODELKIRÎ
Parameters
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 |
06Erêkirin
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.
| Kontrol bikin | How it is done |
|---|---|
| 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.
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.
Kontrol
- Typical annual hazard intensity (location)
- 1.00 intensity index
- Belavbûna nirxên tund (pîvan)
- 0.80 intensity index
- Tundiya ku nîvê nirxê tê de winda dibe
- 4.00 intensity index
- Belavbûna lawazî
- 0.55
- Para nirxê di nav şopa metirsî de
- 40%
- Standarda parastinê (heyama vegerê)
- 50 sal
Xwendin
- Windahiya salane ya navînî
- 0.51% of value
- Windahî di 1 ji 100 salan de
- 24.5% of value
- Windahî di 1 ji 250 salan de
- 28.4% of value
- Tundî di 1 ji 100 salan de
- 4.68 intensity index
Jimar, rêbaz û çavkanî
| Heyama vegerê (sal) | Intensity (intensity index) | Windahî (% ya nirxê) |
|---|---|---|
| 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 |
Rêbaz
- Metirsî: nirxên dawîn ên Gumbel Gumbel (1958), Statistics of Extremes, Columbia University Press
- Nazikiya lognormal (lawazî) FEMA (2003), HAZUS-MH Technical Manual
- Qada îhtîmala derbasbûnê û windahiya salane ya navînî Grossi and Kunreuther (2005), Catastrophe Modeling, Springer
- Bandora bendavê Di Baldassarre and others (2013), Socio-hydrology, HESS 17
- Pankeya nediyarîyê (Monte Carlo ya parametreyan) Spiegelhalter, Pearson and Short (2011), Visualising uncertainty about the future, Science 333
- Hesasiyeta yek-yek (tornado) Saltelli and others (2008), Global Sensitivity Analysis: The Primer, Wiley
Dane
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:
- Çem Natural Earth
- Dirêjahiyên bajarî Natural Earth
- Bajar Natural Earth
- Erdhejên M4.5+, hefteya borî (USGS) U.S. Geological Survey · register usgs.earthquake.summary-feeds
- Rêjeya baranê, nîv saeta dawîn (IMERG) NASA GPM IMERG Early · register nasa.gibs.context-live-layers
- Pêşbînî: herikîna çemê, 30 roj bi navber (GloFAS bi riya Open-Meteo) Open-Meteo.com (CC BY 4.0), Copernicus GloFAS · register open-meteo.public-pages
- Berfirehiya avakirî û niştecihbûnê, 2010 (HBASE, Landsat) CIESIN/Columbia, NASA SEDAC HBASE · register sedac.context-urban-layers
Li seranserê şeş stûnan, bi pêşengiya Nexus Consortium
- Ceribandin Labs
- Hatiye avakirin di Insurance Nexus in Foundry
- Tê ceribandin li Insurance Nexus in Universe
- Hatiye kodkirin di Darayî, sîgorta û aborî di Standards de
- Hatiye weşandin di Insurance Nexus in Reports
- Tê de tê dayîn Fakulteya Darayî û Aborî di Academy de
08Connections
Topics that rely on this method.
09Simulatorê cêwî û kaskade
Trace a shock in extreme value theory for insurance tails to the balance sheet.
Assembled from the Nexus Standards area profile Sîgorta û ji nû ve sîgorta: the shocks it names, the pergalan 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.
Metirsî
- Tropical cyclone
- Erdhej
- Ice-jam flood
- Agirê daristanan
- 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)
- Qutbûna berfireh a elektrîkê (li aliyê jêr çê dibe)
- Koçberiya girseyî (li aliyê jêr çê dibe)
- 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)
Pergal û girêdan
- Sîgorta û ji nû ve sîgorta
- Bankevanî Girêdan
- Saziyên darayiya pêşketinê Girêdan
- Mirovî û civaka sivîl Girêdan
- Çandinî û bikaranîna erdê Girêdan
Kontrol
NS-0Destûr û prensîbNS-3UNIyên tomara xetereyê (rêzimanî, nexşeya veguhastina ji pergala kevin, desthilata veqetandinê)NS-9UNI yên çarçoveyî (belavkirin, mînak, mînakên bernameyê)NS-10Policies and clauses (machine-readable obligations: definition, binding, evaluation and enforcement)NS-11Piştrastkirin û çavdêrî (delîl, erêkirin, çavdêriya lihevhatina zero-trust)NS-14Lihevhatin û nexşeya li standardên derveyîNRS-F3Sîgorta, xetera felaketan û valahiyên parastinêNRS-H113Malbata metirsiyê: Nazikiya pergala darayî (NHS-1 soc.financial-system)NRS-U17Universe platform profile: Insurance NexusNRS-H71Malbata metirsiyê: Felaketên kozmîk û yên dema kûr (NHS-1 planet.deep-time)NRS-H65Malbata metirsiyê: Binpêkirinên sînorên gerstêrkê (NHS-1 planet.boundary)NRS-F8Veguhastina xeterê ya parametrîk û li ser bingeha îndeksê
Çavdêrî
- 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
Erdnîgariya mînakê
- Western Europe: 152 hexagonal cells
- Rêjeya barînê, nîv saeta dawî (IMERG), NASA GIBS
- Ronahiyên şevê îşev, qutbûn (VIIRS Day/Night Band), NASA GIBS
- Ava rûyê erdê di nav ewr re, 30 m (radara OPERA DSWx-S1), NASA GIBS
- Carbon monoxide, smoke transport (AIRS), NASA GIBS
10Stewardship
Who maintains the method.
Sîgortaya duyemîn û katastrof stewards extreme value theory and tail risk for the Consortium and reviews how it is applied across platforms.
11Exposure, loss and capital
What extreme value theory for insurance tails 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 for insurance tails grow with severity, gross and net of reinsurance, against capital.
| Return period | Annual probability | Gross loss | Net loss | Net, capital = 100 |
|---|---|---|---|---|
| 1 in 10 | 0.10 | 14 | 10 | 10 |
| 1 in 50 | 0.02 | 33 | 21 | 21 |
| 1 in 100 | 0.01 | 46 | 27 | 27 |
| 1 in 250 | 0.004 | 68 | 39 | 39 |
| Windahiya salane ya navînî | 3.1 | 2.2 | 2.2 |
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
12Girêdayî
Ev rûpel li ser Konsorsiyûmê te ber bi kû ve dibe.
13Pirs
Pirs û bersiv.
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?
Çavdêrxaneya canonical method page lists every platform that applies it.
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Ji vê rûpelê delîl bidin.
rêzeya Pergalên Stratejîk 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.
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Insurance Nexus
Bring an exposure or capital question to the Alliance.
Agahî û pirs îro vekirî ne. Pirsek referansekê distîne û gava piştî wê dide nasîn; serlêdan, drav, veqetandina hesabkirinê û tomarkirin tenê dema ku tîm, mercên wê û kapasîteya vekolînê hebin vedibin.
Hiqûqî
Belgeyên hiqûqî.
Nexşe, dane û jimarên vê malperê ji bo çarçoveyê û agahiyên giştî têne nîşandan. Ew ne şîret, ne pêşbînî û ne hişyarî ne; sînorên agahiyê di Daxuyaniyên Berpirsiyariyê û Daxuyaniyên Daneyê de hatine diyarkirin.