Extremes

, Volume 4, Issue 2, pp 105–127 | Cite as

Extremal Forex Returns in Extremely Large Data Sets

  • Michel M. Dacorogna
  • Ulrich A. Müller
  • Olivier V. Pictet
  • Casper G. de Vries

Abstract

Exciting information for risk and investment analysis is obtained from an exceptionally large and automatically filtered high frequency data set containing all the forex quote prices on Reuters during a ten-year period. It is shown how the high frequency data improve the efficiency of the tail risk cum loss estimates. We demonstrate theoretically and empirically that the heavy tail feature of foreign exchange rate returns implies that position limits for traders calculated under the industry standard normal model are either not prudent enough, or are overly conservative depending on the time horizon.

extreme value theory regular variation large data sets position limit foreign exchange rates 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baillie, R.T. and Dacorogna, M.M., “Special issue on high frequency data,” Journal of Empirical Finance 4, 69–293, (1997).Google Scholar
  2. Baillie, R.T. and McMahon, P.C., The Foreign Exchange Market, Cambridge University Press, Cambridge, 1989.Google Scholar
  3. Boothe, P. and Glassman, D., “The statistical distribution of exchange rates, empirical evidence and economic implications,” Journal of International Economics 22, 297–319, (1987).Google Scholar
  4. Dacorogna, M.M., Müller, U.A., Nagler, R.J., Olsen, R.B., and Pictet, O.V., “A geographical model for the daily and weekly seasonal volatility in the FX market,” Journal of International Money and Finance 12(4), 413–438, (1993).Google Scholar
  5. Daniclsson, J., de Haan, L, Peng, L., and de Vries, C.G., “Using a bootstrap method to choose the sample fraction in tail index estimation,” Journal of Multivariate Analysis 76, 226–248, (2001).Google Scholar
  6. Danielsson, J. and de Vries, C.G., “Beyond the sample: Extreme quantile and probability estimation with applications to financial data,” Tinbergen Institute, discussion paper, T198-016/2, 1998.Google Scholar
  7. De Haan, L., Jansen, D.W., Koedijk, K.G., and De Vries, C.G., “Safety first portfolio selection, extreme value theory and long run asset risks” In: J. Galambos, J. Lechner, and E. Simiu, (eds), Extreme Value Theory and Applications, Kluwer, Dordrecht, 471–488, (1994).Google Scholar
  8. De Haan, L., Resnick, S.I., Rootzén, H., and De Vries, C.G., “Extremal behavior of solutions to a stochastic difference equation with application to ARCH processes,” Stochastic Processes and their Applications 32, 213–224, (1989).Google Scholar
  9. Dowd, K., Beyond Value at Risk, Wiley, Chichester, 1998.Google Scholar
  10. Drees, H. and Kaufman, E., “Selection of optimal sample fraction in univariate extreme value estimation,” Stochastic Processes and their Applications 75, 149–172, (1998).Google Scholar
  11. Fama, E.F. and Miller, M.H., The Theory of Finance, Dryden Press, Hinsdale, 1972.Google Scholar
  12. Feller, W., An Introduction to Probability Theory and its Applications, Volume II, John Wiley, New York, (second edition), 1971.Google Scholar
  13. Geluk, J., de Haan, L., Resnick, S., and Starica, C., “Second order regular variation, convolution, and the central limit theorem,” Stochastic Processes and their Applications 69, 139–159, (1997).Google Scholar
  14. Goldie, C.M. and Smith, R.L., “Slow variation with remainder: Theory and applications,” Quarterly Journal of Mathematics, Oxford 2nd series, 38, 45–71, (1987).Google Scholar
  15. Goldie, C.M., “Implicit renewal theory and tails of solutions of random equations,” The Annals of Applied Probability 1, 126–166, (1991).Google Scholar
  16. Groenendijk, P.A., Lucas, A., and de Vries, C.G., “A note on the relationship between GARCH and symmetric stable processes,” Journal of Empirical Finance 2, 253–264, (1995).Google Scholar
  17. Hall, P., “On some simple estimates of an exponent of regular variation,” Journal of the Royal Statistical Society Series B, 44, 37–42, (1982).Google Scholar
  18. Hall, P., “Using the bootstrap to estimate mean square error and select smoothing parameter in nonparametric problem,” Journal of Multivariate Analysis 32, 177–203, (1990).Google Scholar
  19. Hill, B.M., “A simple general approach to inference about the tail of a distribution,” The Annals of Statistics 19, 1547–1569, (1975).Google Scholar
  20. Hols, M.C. and De Vries, C.G., “The limiting distributions of extremal exchange rate returns,” Journal of Applied Econometrics 6, 287–302, (1991).Google Scholar
  21. Leadbetter, M.R., Lindgren, G., and Rootzén, H. Extremes and Related Properties of Random Sequences and Processes, Springer-Verlag, Berlin, 1983.Google Scholar
  22. Müller, U.A., Dacorogna, M.M., Olsen, R.B., Pictet, O.V., Schwarz, M., and Morgenegg, C., “Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis,” Journal of Banking and Finance 14, 1189–1208, (1990).Google Scholar
  23. Stahl, G., “Three cheers,” Risk 10, 67–69, (1997).Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Michel M. Dacorogna
    • 1
  • Ulrich A. Müller
    • 2
  • Olivier V. Pictet
    • 3
  • Casper G. de Vries
    • 4
  1. 1.Zurich Insurance Company, ReinsuranceSwitzerland
  2. 2.Research Institute for Applied EconomicsOlsen and AssociatesSwitzerland
  3. 3.Dynamic Asset Management SASwitzerland
  4. 4.Tinbergen InstituteErasmus Universiteit RotterdamThe Netherlands

Personalised recommendations