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Calibrating Distribution Models from PELVE

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  • Hirbod Assa
  • Liyuan Lin
  • Ruodu Wang

Abstract

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 article, we study the converse problem of PELVE calibration; that is, to find a distribution model that yields a given PELVE, which may be obtained either 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.

Suggested Citation

  • Hirbod Assa & Liyuan Lin & Ruodu Wang, 2024. "Calibrating Distribution Models from PELVE," North American Actuarial Journal, Taylor & Francis Journals, vol. 28(2), pages 373-406, April.
    • Handle: RePEc:taf:uaajxx:v:28:y:2024:i:2:p:373-406
    DOI: 10.1080/10920277.2023.2211648
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    Cited by:

    1. Agrawal, Srishti & Seth, Adit & Goel, Rahul, 2024. "A silent revolution: Rapid rise of cycling to school in rural India," Journal of Transport Geography, Elsevier, vol. 119(C).

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