Generating unfavourable VaR scenarios with patchwork copulas

TL;DR

This paper introduces a simple patchwork copula method to generate adverse VaR scenarios in multivariate models, aiding insurance risk assessment under regulatory standards.

Contribution

It proposes a novel, straightforward patchwork copula construction for creating unfavourable VaR scenarios while preserving marginal distributions.

Findings

Effective in 19-dimensional insurance loss data

Maintains marginal distributions during scenario generation

Facilitates internal model development for Solvency II

Abstract

The central idea of the paper is to present a general simple patchwork construction principle for multivariate copulas that create unfavourable VaR (i.e. Value at Risk) scenarios while maintaining given marginal distributions. This is of particular interest for the construction of Internal Models in the insurance industry under Solvency II in the European Union. The method is exemplified with a 19-dimensional real-life data set of insurance losses.