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Time-inconsistency of VaR and time-consistent alternatives

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  • Cheridito, Patrick
  • Stadje, Mitja

Abstract

We show that VaR (Value-at-Risk) is not time-consistent and discuss examples where this can lead to dynamically inconsistent behavior. Then we propose two time-consistent alternatives to VaR. The first one is a composition of one-period VaR's. It is time-consistent but not coherent. The second one is a composition of average VaR's. It is a time-consistent coherent risk measure.

Suggested Citation

  • Cheridito, Patrick & Stadje, Mitja, 2009. "Time-inconsistency of VaR and time-consistent alternatives," Finance Research Letters, Elsevier, vol. 6(1), pages 40-46, March.
  • Handle: RePEc:eee:finlet:v:6:y:2009:i:1:p:40-46
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Boucher, Christophe M. & Daníelsson, Jón & Kouontchou, Patrick S. & Maillet, Bertrand B., 2014. "Risk models-at-risk," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 72-92.
    2. Engsner, Hampus & Lindholm, Mathias & Lindskog, Filip, 2017. "Insurance valuation: A computable multi-period cost-of-capital approach," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 250-264.
    3. Pelsser, Antoon & Salahnejhad Ghalehjooghi, Ahmad, 2016. "Time-consistent actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 97-112.
    4. Hampus Engsner & Mathias Lindholm & Filip Lindskog, 2016. "Insurance valuation: a computable multi-period cost-of-capital approach," Papers 1607.04100, arXiv.org.
    5. Daniel, Engelage, 2011. "Optimal stopping with dynamic variational preferences," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2042-2074, September.
    6. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2016. "A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective," Papers 1603.09030, arXiv.org, revised Jan 2017.
    7. Zachary Feinstein & Birgit Rudloff, 2012. "Time consistency of dynamic risk measures in markets with transaction costs," Papers 1201.1483, arXiv.org, revised Dec 2012.
    8. Zachary Feinstein & Birgit Rudloff, 2012. "Multiportfolio time consistency for set-valued convex and coherent risk measures," Papers 1212.5563, arXiv.org, revised Oct 2014.
    9. Claudia Kluppelberg & Jianing Zhang, 2015. "Time-consistency of risk measures with GARCH volatilities and their estimation," Papers 1504.04774, arXiv.org, revised Feb 2016.
    10. Wayne King Ming Chan, 2015. "RAROC-Based Contingent Claim Valuation," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 21.
    11. Zachary Feinstein & Birgit Rudloff, 2015. "Multi-portfolio time consistency for set-valued convex and coherent risk measures," Finance and Stochastics, Springer, vol. 19(1), pages 67-107, January.
    12. Hellmann, Tobias & Riedel, Frank, 2015. "A dynamic extension of the Foster–Hart measure of riskiness," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 66-70.
    13. Pierre Devolder & Adrien Lebègue, 2016. "Compositions of Conditional Risk Measures and Solvency Capital," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-21, December.
    14. Zachary Feinstein & Birgit Rudloff, 2015. "A Supermartingale Relation for Multivariate Risk Measures," Papers 1510.05561, arXiv.org, revised Jan 2018.
    15. repec:dau:papers:123456789/15232 is not listed on IDEAS
    16. Klüppelberg Claudia & Zhang Jianing, 2016. "Time-consistency of risk measures with GARCH volatilities and their estimation," Statistics & Risk Modeling, De Gruyter, vol. 32(2), pages 103-124, March.

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