Quantum Risk Analysis: Beyond (Conditional) Value-at-Risk

TL;DR

This paper develops quantum algorithms for alternative risk measures like EVaR and RVaR, compares their performance with existing quantum VaR and CVaR algorithms, and evaluates their robustness on simulators and real devices.

Contribution

It introduces quantum algorithms for EVaR and RVaR, expanding quantum risk analysis beyond traditional VaR and CVaR measures.

Findings

All algorithms perform well on quantum simulators.

EVaR and VaR calculations are robust against noise on real quantum devices.

CVaR and RVaR are less robust to noise on real quantum devices.

Abstract

Risk measures are important key figures to measure the adequacy of the reserves of a company. The most common risk measures in practice are Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). Recently, quantum-based algorithms are introduced to calculate them. These procedures are based on the so-called quantum amplitude estimation algorithm which lead to a quadratic speed up compared to classical Monte-Carlo based methods. Based on these ideas, we construct quantum-based algorithms to calculate alternatives for VaR and CVaR, namely the Expectile Value-at-Risk (EVaR) and the Range Value-at-Risk (RVaR). We construct quantum algorithms to calculate them. These algorithms are based on quantum amplitude estimation. In a case study, we compare their performance with the quantum-based algorithms for VaR and CVaR. We find that all of the algorithms perform sufficiently well on a quantum simulator. Further, the calculations of EVaR and VaR are robust against noise on a real quantum device. This is not the case for CVaR and RVaR.