Research library

INVESTIGATION 05 / MARKET & TAIL RISK

Learning from the tail

What can the most extreme observations tell us?

Extreme value theoryGPDThreshold sensitivity

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.

The analyst’s decision

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 result

Evidence record: research-validation.json#numerical_checks/05

Explore the related lab

04 / 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

Loading validation evidence…

Interpretation limit

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