Extreme value theory and tail risk
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. Reinsurance and Catastrophe stewards this page for the Nexus Consortium.
- Institution
- The Global Centre for Risk and Innovation (GCRI)
- Service level
- R0: information and enquiries
Tail fit
GCRI · Extreme value theory and tail risk · Run R-5442
Return level curve
Method card
- Method
- Extreme value theory and…
- Approach
- peaks over threshold
- Threshold
- 90th percentile
- Label
- MODELLED
Parameters
generalised Pareto fit
| Shape ξ | 0.25 | −0.02 | 0.51 | heavy tail if above zero |
| Scale σ | 2.7 | 1.1 | 6.6 | units of the variable |
| Exceedances | 62 | declustered |
GCRI · Tail fitTail fit, in outline: domain structure with placeholder names and illustrative values, not a record.
The short answer.
Extreme value theory and tail risk study the behaviour of rare, high-impact events. Extreme value methods set design levels and capital buffers for rare events. In the Nexus Consortium, Reinsurance and Catastrophe stewards its canonical page, and 5 other platforms apply it, including Water Nexus as well as Climate and Hazards.
Systemic exposure in the Caribbean.
Where people and networks concentrate, the exposure through which shocks travel between systems, shown for the Caribbean as an example geography for this subject.
What extreme value theory and tail risk covers.
- 01
Core methods
block maxima analysis; peaks over threshold modelling; return level estimation; multivariate extremes; non-stationary extreme value models; tail dependence analysis.
- 02
Data and instruments
long hydrometeorological records; insurance loss histories; financial return series; paleo and historical event records; climate model ensembles.
- 03
Validation
Fits are checked with diagnostic plots, goodness-of-fit tests and out-of-sample comparison. Sensitivity to threshold and record length is reported.
- 04
Limits
Extrapolation far beyond the data is highly uncertain. Changing climates and markets violate stationarity assumptions.
- 05
Use in risk decisions
Extreme value methods set design levels and capital buffers for rare events. Tail dependence analysis reveals when extremes in different systems tend to occur together.
Extreme value analysis is standard in hydrology, climate and actuarial practice.
| Reference | What it sets |
|---|---|
| WMO guidance on extremes | Analysis of climate extremes |
| Flood frequency analysis practice | Design floods in national guidance |
| Actuarial and solvency standards | Tail risk measures |
Tails that move together.
Extreme value theory estimates the probability of events beyond observed records. In systemic analysis two issues dominate: non-stationarity (the tail is moving) and tail dependence (extremes in different places or variables occurring together). Both widen uncertainty considerably.
- Fit non-stationary models where trends exist.
- Estimate tail dependence, not only correlation.
- Report return-level uncertainty.
- Applications on Water Nexus and Climate and Hazards.
Who maintains this page.
Reinsurance and Catastrophe stewards extreme value theory and tail risk: it keeps this description current and reviews how the method is applied across the platforms.
Terms used on this page.
Each term as this page uses it. Where a standard-setting body defines the term, the wording follows that body.
| Term | Definition |
|---|---|
| Value at risk | The loss that will not be exceeded with a stated probability over a stated period, such as one year. |
| Expected shortfall | The average loss in the worst cases beyond a stated probability level, which captures the size of the tail that value at risk ignores. |
| Generalised Pareto distribution | The distribution used to model losses above a high threshold in the peaks-over-threshold method. |
| Tail dependence | The tendency of two risks to suffer extreme losses together more often than their ordinary correlation suggests. |
Where this page's references lead.
The bodies and documents this page is read against. Status and editions change; each link goes to the issuing body.
Where this page leads across the Consortium.
- Extreme value statistics for floods and droughtsGCRIApplied in Water Nexus.
- Extreme value statistics for hazardsGCRIApplied in Climate and Hazards.
- Extreme value statistics for coastsGCRIApplied in Oceans and Coasts.
- Extreme value theory for insurance tailsGRAApplied in Insurance Nexus.
- Extreme value theory and tail risk for reinsurance and catastropheGRAApplied in Reinsurance and Catastrophe.
- Extreme value theory and tail risk for actuarial and quantitative riskGRAApplied in Actuarial and Quantitative Risk.
Questions and answers.
Why does one institution host every method page?
How do I suggest a correction to a method page?
Around GCRI.
Start with an enquiry.
The current service level is R0: information and enquiries. An enquiry receives a reference and names the next step; applications, payments, compute allocations and registrations open only when their team, terms and review capacity exist.