IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2204.08882.html
   My bibliography  Save this paper

Calibrating distribution models from PELVE

Author

Listed:
  • 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 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.

Suggested Citation

  • Hirbod Assa & Liyuan Lin & Ruodu Wang, 2022. "Calibrating distribution models from PELVE," Papers 2204.08882, arXiv.org, revised Jun 2023.
  • Handle: RePEc:arx:papers:2204.08882
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2204.08882
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    2. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    3. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
    4. Paul Embrechts & Giovanni Puccetti & Ludger Rüschendorf & Ruodu Wang & Antonela Beleraj, 2014. "An Academic Response to Basel 3.5," Risks, MDPI, vol. 2(1), pages 1-24, February.
    5. Christopher P. Chambers, 2009. "An Axiomatization Of Quantiles On The Domain Of Distribution Functions," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 335-342, April.
    6. Krause, Daniel & Scherer, Matthias & Schwinn, Jonas & Werner, Ralf, 2018. "Membership testing for Bernoulli and tail-dependence matrices," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 240-260.
    7. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    8. Paul Embrechts & Haiyan Liu & Tiantian Mao & Ruodu Wang, 2017. "Quantile-Based Risk Sharing with Heterogeneous Beliefs," Swiss Finance Institute Research Paper Series 17-65, Swiss Finance Institute, revised Jan 2018.
    9. Matthew Norton & Valentyn Khokhlov & Stan Uryasev, 2021. "Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation," Annals of Operations Research, Springer, vol. 299(1), pages 1281-1315, April.
    10. Ruodu Wang & Ričardas Zitikis, 2021. "An Axiomatic Foundation for the Expected Shortfall," Management Science, INFORMS, vol. 67(3), pages 1413-1429, March.
    11. Susanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What is the best risk measure in practice? A comparison of standard measures," Papers 1312.1645, arXiv.org, revised Apr 2015.
    12. L. Berezansky & E. Braverman, 2011. "On Nonoscillation of Advanced Differential Equations with Several Terms," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-14, March.
    13. Matyas Barczy & Fanni K. Ned'enyi & L'aszl'o SutH{o}, 2022. "Probability equivalent level of Value at Risk and higher-order Expected Shortfalls," Papers 2202.09770, arXiv.org, revised Nov 2022.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xia Han & Liyuan Lin & Ruodu Wang, 2022. "Diversification quotients: Quantifying diversification via risk measures," Papers 2206.13679, arXiv.org, revised Jul 2024.
    2. Ruodu Wang & Ričardas Zitikis, 2021. "An Axiomatic Foundation for the Expected Shortfall," Management Science, INFORMS, vol. 67(3), pages 1413-1429, March.
    3. Xia Han & Liyuan Lin & Ruodu Wang, 2023. "Diversification quotients based on VaR and ES," Papers 2301.03517, arXiv.org, revised May 2023.
    4. Han, Xia & Lin, Liyuan & Wang, Ruodu, 2023. "Diversification quotients based on VaR and ES," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 185-197.
    5. Bellini, Fabio & Fadina, Tolulope & Wang, Ruodu & Wei, Yunran, 2022. "Parametric measures of variability induced by risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 270-284.
    6. Tobias Fissler & Fangda Liu & Ruodu Wang & Linxiao Wei, 2024. "Elicitability and identifiability of tail risk measures," Papers 2404.14136, arXiv.org, revised Jun 2024.
    7. Paul Embrechts & Alexander Schied & Ruodu Wang, 2018. "Robustness in the Optimization of Risk Measures," Papers 1809.09268, arXiv.org, revised Feb 2021.
    8. Ruodu Wang & Yunran Wei, 2020. "Risk functionals with convex level sets," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1337-1367, October.
    9. Fissler Tobias & Ziegel Johanna F., 2021. "On the elicitability of range value at risk," Statistics & Risk Modeling, De Gruyter, vol. 38(1-2), pages 25-46, January.
    10. Tolulope Fadina & Yang Liu & Ruodu Wang, 2021. "A Framework for Measures of Risk under Uncertainty," Papers 2110.10792, arXiv.org, revised Sep 2023.
    11. Li, Hengxin & Wang, Ruodu, 2023. "PELVE: Probability Equivalent Level of VaR and ES," Journal of Econometrics, Elsevier, vol. 234(1), pages 353-370.
    12. Edgars Jakobsons & Steven Vanduffel, 2015. "Dependence Uncertainty Bounds for the Expectile of a Portfolio," Risks, MDPI, vol. 3(4), pages 1-25, December.
    13. Tobias Fissler & Jana Hlavinová & Birgit Rudloff, 2021. "Elicitability and identifiability of set-valued measures of systemic risk," Finance and Stochastics, Springer, vol. 25(1), pages 133-165, January.
    14. Hirbod Assa & Peng Liu, 2024. "Factor risk measures," Papers 2404.08475, arXiv.org.
    15. Xia Han & Qiuqi Wang & Ruodu Wang & Jianming Xia, 2021. "Cash-subadditive risk measures without quasi-convexity," Papers 2110.12198, arXiv.org, revised May 2024.
    16. Fabio Bellini & Tolulope Fadina & Ruodu Wang & Yunran Wei, 2020. "Parametric measures of variability induced by risk measures," Papers 2012.05219, arXiv.org, revised Apr 2022.
    17. Fangyuan Zhang, 2023. "Non-concave portfolio optimization with average value-at-risk," Mathematics and Financial Economics, Springer, volume 17, number 3, October.
    18. Paul Embrechts & Tiantian Mao & Qiuqi Wang & Ruodu Wang, 2021. "Bayes risk, elicitability, and the Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1190-1217, October.
    19. Haiyan Liu & Bin Wang & Ruodu Wang & Sheng Chao Zhuang, 2023. "Distorted optimal transport," Papers 2308.11238, arXiv.org.
    20. Ruodu Wang & Johanna F. Ziegel, 2021. "Scenario-based risk evaluation," Finance and Stochastics, Springer, vol. 25(4), pages 725-756, October.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2204.08882. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.