Generating VaR scenarios with product beta distributions

TL;DR

This paper introduces a Monte Carlo simulation method using product beta distributions to generate VaR scenarios for dependent risks under Solvency II, aiding in stress testing and internal model development.

Contribution

It presents a novel approach for joint density estimation using product beta distributions, improving stress test scenario generation for dependent risks.

Findings

Effective generation of VaR scenarios for dependent risks

Application to Solvency II stress testing requirements

Enhanced internal model construction methods

Abstract

We propose a Monte Carlo simulation method to generate stress tests by VaR scenarios under Solvency II for dependent risks on the basis of observed data. This is of particular interest for the construction of Internal Models and requirements on evaluation processes formulated in the Commission Delegated Regulation. The approach is based on former work on partition-ofunity copulas, however with a direct scenario estimation of the joint density by product beta distributions after a suitable transformation of the original data.