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Multivariate extremes, aggregation and risk estimation

Author

Listed:
  • H. A. Hauksson
  • M. Dacorogna
  • T. Domenig
  • U. Mller
  • G. Samorodnitsky

Abstract

We briefly introduce some basic facts about multivariate extreme value theory and present some new results regarding finite aggregates and multivariate extreme value distributions. Based on our results high-frequency data can considerably improve the quality of estimates of extreme movements in financial markets. Secondly, we present an empirical exploration of what the tails really look like for four foreign exchange rates sampled at varying frequencies. Both temporal and spatial dependence is considered. In particular we estimate the spectral measure, which along with the tail index, completely determines the extreme value distribution. Lastly, we apply our results to the problem of portfolio optimization or risk minimization. We analyse how the expected shortfall and value-at-risk scale with the time horizon and find that this scaling is not by a factor of the square root of time as is frequently used, but by a different power of time. We show that the accuracy of risk estimation can be drastically improved by using hourly or bihourly data.

Suggested Citation

  • H. A. Hauksson & M. Dacorogna & T. Domenig & U. Mller & G. Samorodnitsky, 2001. "Multivariate extremes, aggregation and risk estimation," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 79-95.
    • Handle: RePEc:taf:quantf:v:1:y:2001:i:1:p:79-95
    DOI: 10.1080/713665553
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    Cited by:

    1. Suzanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What Is the Best Risk Measure in Practice? A Comparison of Standard Measures," Working Papers hal-00921283, HAL.
    2. Georg Mainik & Ludger Rüschendorf, 2010. "On optimal portfolio diversification with respect to extreme risks," Finance and Stochastics, Springer, vol. 14(4), pages 593-623, December.
    3. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    4. repec:hal:journl:hal-00921283 is not listed on IDEAS
    5. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
    6. Polanski, Arnold & Stoja, Evarist, 2017. "Forecasting multidimensional tail risk at short and long horizons," International Journal of Forecasting, Elsevier, vol. 33(4), pages 958-969.
    7. Polanski, Arnold & Stoja, Evarist, 2017. "Forecasting multidimensional tail risk at short and long horizons," Bank of England working papers 660, Bank of England.
    8. Einmahl, J.H.J. & de Haan, L.F.M. & Piterbarg, V.I., 2001. "Nonparametric estimation of the spectral measure of an extreme value distribution," Other publications TiSEM c3485b9b-a0bd-456f-9baa-0, Tilburg University, School of Economics and Management.
    9. Gilles Zumbach, 2011. "Characterizing heteroskedasticity," Quantitative Finance, Taylor & Francis Journals, vol. 11(9), pages 1357-1369, October.
    10. Polanski, Arnold & Stoja, Evarist, 2014. "Co-dependence of extreme events in high frequency FX returns," Journal of International Money and Finance, Elsevier, vol. 44(C), pages 164-178.
    11. Falk, Michael, 2005. "On the generation of a multivariate extreme value distribution with prescribed tail dependence parameter matrix," Statistics & Probability Letters, Elsevier, vol. 75(4), pages 307-314, December.
    12. Härdle, Wolfgang Karl & Spokoiny, Vladimir & Wang, Weining, 2010. "Local quantile regression," SFB 649 Discussion Papers 2011-005, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. Schmidt, Rafael & Hrycej, Tomas & Stutzle, Eric, 2006. "Multivariate distribution models with generalized hyperbolic margins," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 2065-2096, April.
    14. 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.
    15. Jing Ai & Patrick L. Brockett & Tianyang Wang, 2017. "Optimal Enterprise Risk Management and Decision Making With Shared and Dependent Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(4), pages 1127-1169, December.
    16. Gencay, Ramazan & Selcuk, Faruk & Ulugulyagci, Abdurrahman, 2003. "High volatility, thick tails and extreme value theory in value-at-risk estimation," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 337-356, October.
    17. Richards, Jordan & Tawn, Jonathan A., 2022. "On the tail behaviour of aggregated random variables," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    18. Y. Malevergne & D. Sornette, 2002. "Investigating Extreme Dependences: Concepts and Tools," Papers cond-mat/0203166, arXiv.org.
    19. Aleksy Leeuwenkamp & Wentao Hu, 2023. "New general dependence measures: construction, estimation and application to high-frequency stock returns," Papers 2309.00025, arXiv.org.
    20. Peter Blum & Michel Dacorogna & Lars Jaeger, 2003. "Performance and Risk Measurement Challenges For Hedge Funds: Empirical Considerations," Risk and Insurance 0311001, University Library of Munich, Germany.

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