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On the properties of the Lambda value at risk: robustness, elicitability and consistency

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  • Matteo Burzoni
  • Ilaria Peri
  • Chiara Maria Ruffo

Abstract

Recently, financial industry and regulators have enhanced the debate on the good properties of a risk measure. A fundamental issue is the evaluation of the quality of a risk estimation. On the one hand, a backtesting procedure is desirable for assessing the accuracy of such an estimation and this can be naturally achieved by elicitable risk measures. For the same objective, an alternative approach has been introduced by Davis (2016) through the so-called consistency property. On the other hand, a risk estimation should be less sensitive with respect to small changes in the available data set and exhibit qualitative robustness. A new risk measure, the Lambda value at risk (Lambda VaR), has been recently proposed by Frittelli et al. (2014), as a generalization of VaR with the ability to discriminate the risk among P&L distributions with different tail behaviour. In this article, we show that Lambda VaR also satisfies the properties of robustness, elicitability and consistency under some conditions.

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  • Matteo Burzoni & Ilaria Peri & Chiara Maria Ruffo, 2016. "On the properties of the Lambda value at risk: robustness, elicitability and consistency," Papers 1603.09491, arXiv.org, revised Feb 2017.
    • Handle: RePEc:arx:papers:1603.09491
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    Cited by:

    1. Silvana M. Pesenti & Steven Vanduffel, 2023. "Optimal Transport Divergences induced by Scoring Functions," Papers 2311.12183, arXiv.org, revised Apr 2024.
    2. Tim J. Boonen & Yuyu Chen & Xia Han & Qiuqi Wang, 2024. "Optimal insurance design with Lambda-Value-at-Risk," Papers 2408.09799, arXiv.org.
    3. Matthias Fischer & Thorsten Moser & Marius Pfeuffer, 2018. "A Discussion on Recent Risk Measures with Application to Credit Risk: Calculating Risk Contributions and Identifying Risk Concentrations," Risks, MDPI, vol. 6(4), pages 1-28, December.
    4. Javier Ojea-Ferreiro, 2021. "Deconstructing Systemic Risk: A Reverse Stress Testing Approach," Springer Books, in: Marco Corazza & Manfred Gilli & Cira Perna & Claudio Pizzi & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 369-375, Springer.
    5. Fabio Bellini & Ilaria Peri, 2021. "An axiomatization of $\Lambda$-quantiles," Papers 2109.02360, arXiv.org, revised Jan 2022.
    6. Christopher P. Chambers & Alan D. Miller, 2023. "Multiple Adjusted Quantiles," Papers 2305.06354, arXiv.org.
    7. Owusu Junior, Peterson & Alagidede, Imhotep, 2020. "Risks in emerging markets equities: Time-varying versus spatial risk analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    8. Xia Han & Peng Liu, 2024. "Robust Lambda-quantiles and extreme probabilities," Papers 2406.13539, arXiv.org.
    9. Valeria Bignozzi & Matteo Burzoni & Cosimo Munari, 2020. "Risk Measures Based on Benchmark Loss Distributions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 87(2), pages 437-475, June.
    10. Akif Ince & Ilaria Peri & Silvana Pesenti, 2021. "Risk contributions of lambda quantiles," Papers 2106.14824, arXiv.org, revised Nov 2022.
    11. Asmerilda Hitaj & Cesario Mateus & Ilaria Peri, 2018. "Lambda Value at Risk and Regulatory Capital: A Dynamic Approach to Tail Risk," Risks, MDPI, vol. 6(1), pages 1-18, March.
    12. Peng Liu & Andreas Tsanakas & Yunran Wei, 2024. "Risk sharing with Lambda value at risk under heterogeneous beliefs," Papers 2408.03147, arXiv.org, revised Sep 2024.

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