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Multivariate extremes, aggregation and risk estimation

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Author Info

  • Michel Dacorogna

    (Zürich Re)

  • Höskuldur Ari Hauksson
  • Thomas Domenig
  • Ulrich Müller
  • Gennady 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 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 optimisation or risk minimization. We analyze how the expected shortfall and VaR scale with time horizon and find that this scaling is not by a factor of 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.

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Bibliographic Info

Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Workshop Papers, January 2001 with number P2.

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Date of creation: 04 Jan 2001
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Handle: RePEc:ams:cdws01:p2

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Postal: Dept. of Economics and Econometrics, Universiteit van Amsterdam, Roetersstraat 11, NL - 1018 WB Amsterdam, The Netherlands
Phone: + 31 20 525 52 58
Fax: + 31 20 525 52 83
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Web page: http://www.fee.uva.nl/cendef/
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Cited by:
  1. Faruk Selcuk & Ramazan Gencay, 2001. "Overnight Borrowing, Interest Rates and Extreme Value Theory," Departmental Working Papers 0103, Bilkent University, Department of Economics.
  2. Arnold Polanski & Evarist Stoja, 2013. "Co-dependence of Extreme Events in High Frequency FX Returns," University of East Anglia Applied and Financial Economics Working Paper Series 040, School of Economics, University of East Anglia, Norwich, UK..
  3. Peter Blum & Michel Dacorogna & Lars Jaeger, 2003. "Performance and Risk Measurement Challenges For Hedge Funds: Empirical Considerations," Risk and Insurance 0311001, EconWPA.
  4. 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.
  5. 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 Dec 2013.
  6. Suzanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What Is the Best Risk Measure in Practice? A Comparison of Standard Measures," Post-Print hal-00921283, HAL.
  7. Y. Malevergne & D. Sornette, 2002. "Investigating Extreme Dependences: Concepts and Tools," Papers cond-mat/0203166, arXiv.org.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Ardia, David, 2003. "Analysis of dependencies in low frequency financial data sets," MPRA Paper 12682, University Library of Munich, Germany.
  13. 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.

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