Examples¶

Fourteen scripts in examples/, each of which runs and asserts its own claims — so they cannot drift out of date without failing.

python examples/04_tail_dependence.py
pytest tests/test_examples.py     # run them all

Foundations¶


01	Build a copula, evaluate it, sample it
02	Sklar's theorem both ways; the Fréchet bounds
03	What each dependence measure sees, and what it misses
04	Tail dependence: what τ does not tell you


05	Five estimators, and standard errors that are calibrated
06	Goodness of fit, family selection, cross-validation


07	Portfolio VaR, expected shortfall, CoVaR, stress testing
08	CDO tranches, the correlation skew, the 2008 failure mode
09	Basket, rainbow, spread and CMS spread options
10	Pairs trading on conditional copula probabilities
11	Copula-GARCH: volatility in time, dependence in the cross-section
12	Operational-risk capital, reinsurance layers, cat bonds
28	How-to: a vine copula on market returns, step by step
29	How-to: risk management for a multi-desk book
30	How-to: copula trading strategies, pairs to vine baskets
31	How-to: valuing odd assets under different tails
32	How-to: copulas for an 800-stock basket


13	Kendall return periods for flood frequency
14	Asymmetric dependence and both-tail mixtures

All at identical Kendall's τ, so none of it is visible to a rank correlation:

Six families, two-line loss portfolio: 99% ES spans 29%, and plain Clayton lands below the Gaussian.
CDO senior tranche, t copula vs Gaussian: 3× worse.
Operational risk across seven cells: Gumbel costs 20% more capital.
Flood frequency, five families: Kendall return periods span a factor of 33.