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Multivariate extremes, aggregation and risk estimation

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Author Info

  • 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.

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Bibliographic Info

Article provided by Taylor and Francis Journals in its journal Quantitative Finance.

Volume (Year): 1 (2001)
Issue (Month): 1 ()
Pages: 79-95
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Handle: RePEc:taf:quantf:v:1:y:2001:i:1:p:79-95

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Cited by:
  1. 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.
  2. 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.
  3. Y. Malevergne & D. Sornette, 2002. "Investigating Extreme Dependences: Concepts and Tools," Quantitative Finance Papers cond-mat/0203166, arXiv.org.
  4. 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.
  5. Faruk Selcuk & Ramazan Gencay, 2001. "Overnight Borrowing, Interest Rates and Extreme Value Theory," Departmental Working Papers 0103, Bilkent University, Department of Economics.
  6. Ardia, David, 2003. "Analysis of dependencies in low frequency financial data sets," MPRA Paper 12682, University Library of Munich, Germany.
  7. Peter Blum & Michel Dacorogna & Lars Jaeger, 2003. "Performance and Risk Measurement Challenges For Hedge Funds: Empirical Considerations," Risk and Insurance 0311001, EconWPA.

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