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Lambda Value at Risk and Regulatory Capital: A Dynamic Approach to Tail Risk

Author

Listed:
  • Asmerilda Hitaj

    (Department of Statistics and Quantitative Methods, University of Milan Bicocca, U7, Via Bicocca degli Arcimboldi 8, Milan 20126, Italy)

  • Cesario Mateus

    (Department of Accounting and Finance, University of Greenwich, Old Royal Naval College, Park Row, London SE10 9LS, UK)

  • Ilaria Peri

    (Department of Economics, Mathematics and Statistics, Birkbeck University of London, Malet St, Bloomsbury, London WC1E 7HX, UK)

Abstract

This paper presents the first methodological proposal of estimation of the Λ V a R . Our approach is dynamic and calibrated to market extreme scenarios, incorporating the need of regulators and financial institutions in more sensitive risk measures. We also propose a simple backtesting methodology by extending the V a R hypothesis-testing framework. Hence, we test our Λ V a R proposals under extreme downward scenarios of the financial crisis and different assumptions on the profit and loss distribution. The findings show that our Λ V a R estimations are able to capture the tail risk and react to market fluctuations significantly faster than the V a R and expected shortfall. The backtesting exercise displays a higher level of accuracy for our Λ V a R estimations.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:1:p:17-:d:134856
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    References listed on IDEAS

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    1. M. Burzoni & I. Peri & C. M. Ruffo, 2017. "On the properties of the Lambda value at risk: robustness, elicitability and consistency," Quantitative Finance, Taylor & Francis Journals, vol. 17(11), pages 1735-1743, November.
    2. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, vol. 57(12), pages 2213-2227, December.
    3. 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.
    4. Robert Engle, 2001. "GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 157-168, Fall.
    5. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    6. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    7. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    8. Jacopo Corbetta & Ilaria Peri, 2016. "Backtesting Lambda Value at Risk," Papers 1602.07599, arXiv.org, revised Jun 2017.
    9. 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.
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    Citations

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    Cited by:

    1. Tim J. Boonen & Yuyu Chen & Xia Han & Qiuqi Wang, 2024. "Optimal insurance design with Lambda-Value-at-Risk," Papers 2408.09799, arXiv.org.
    2. 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.
    3. 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.
    4. Fabio Bellini & Ilaria Peri, 2021. "An axiomatization of $\Lambda$-quantiles," Papers 2109.02360, arXiv.org, revised Jan 2022.
    5. Xia Han & Peng Liu, 2024. "Robust Lambda-quantiles and extreme probabilities," Papers 2406.13539, arXiv.org.
    6. Akif Ince & Ilaria Peri & Silvana Pesenti, 2021. "Risk contributions of lambda quantiles," Papers 2106.14824, arXiv.org, revised Nov 2022.
    7. 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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