Copula-Tail VaR Engine

A multi-asset tail-risk engine that blends Student-t copulas with Peak-Over-Threshold extreme value marginals to estimate 99% Expected Shortfall far more accurately than historical simulation.

Python SciPy / NumPy EVT / POT t-Copula Risk

Documentation Demo GitHub

Problem

Historical simulation can only replay observed losses and estimates the 99% quantile from a handful of points — noisy and biased in the tail.

Method

EVT/GPD marginals model each asset's fat tail; a Student-t copula captures tail co-movement. Monte Carlo aggregates into VaR and ES.

Result

≈30% reduction in absolute 99% ES error (measured 30.43%) versus a bootstrap historical baseline on synthetic ground-truth data.

Highlights

Student-t copula with automatic degrees-of-freedom optimisation and positive-definite correlation projection.
Hybrid marginals: empirical body spliced to a GPD tail, with a graceful empirical fallback for thin data.
Reproducible synthetic market generator with a known data-generating process for exact benchmarking.
Pytest suite validating EVT inverse consistency, copula likelihood gains, and the ≥30% ES-error improvement.