2022/04/19 by Hirbod Assa, Liyuan Lin, Assa, Hirbod +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #FOS: Economics and business #Financial Risk and Volatility Modeling #Insurance and Financial Risk Management #Probability and Risk Models #Risk Management (q-fin.RM)
paper · pdf · doi:10.48550/arxiv.2204.08882
openalex publication_date 2022/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The Value-at-Risk (VaR) and the Expected Shortfall (ES) are the two most popular risk measures in banking and insurance regulation. To bridge between the two regulatory risk measures, the Probability Equivalent Level of VaR-ES (PELVE) was recently proposed to convert a level of VaR to that of ES. It is straightforward to compute the value of PELVE for a given distribution model. In this paper, we study the converse problem of PELVE calibration, that is, to find a distribution model that yields a given PELVE, which may either be obtained from data or from expert opinion. We discuss separately the cases when one-point, two-point, n-point and curve constraints are given. In the most complicated case of a curve constraint, we convert the calibration problem to that of an advanced differential equation. We apply the model calibration techniques to estimation and simulation for datasets used in insurance. We further study some technical properties of PELVE by offering a few new results on monotonicity and convergence.