01 / THE PRACTICAL QUESTION
A decision, before a model.
The few worst losses matter most for a tail estimate, but there may be too few of them to estimate an extreme percentile directly.
Choose a tail threshold and inspect how sensitive the estimate is to that choice.
02 / DATA & COMPARISON
The idea in plain language.
Extreme value theory fits excess losses above a threshold. A lower threshold gives more observations but may include losses that do not yet behave like the tail.
- Tail shape
- A parameter describing how slowly the probability of very large losses declines.
Data. Loss exceedances from seeded heavy-tailed samples.
Baseline. Empirical quantiles using the same loss sample.
03 / THE EXPERIMENT
What the saved experiment shows.
For the saved Pareto sample, estimated 99% VaR is 4.737 versus analytical 4.642; estimated ES is 7.319 versus 6.962. The fitted tail shape is 0.352 against a generating value of one third.
Inspect the supporting resultEvidence record: research-validation.json#numerical_checks/05
Explore the related lab04 / RESULTS & LIMITATIONS
Evidence with its boundaries attached.
The related lab is a cross-project demonstration. Read this investigation’s evidence and limits before transferring its conclusions.
Inspect numerical checks and validation records
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Extreme quantiles are sensitive to thresholds, dependence, and limited tail observations.
05 / REPRODUCE
Reproduce and challenge the result.
Code, configuration, and reproduction
The project contains its implementation, configuration, tests, and walkthrough. Download the lab configuration to record the exact parameters used in an interactive run.
Project code and walkthrough