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Origins of scaling in FX markets

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  • Mercik, Szymon
  • Weron, Rafal

Abstract

Typical data sets employed by economists and financial analysts do not exceed a few hundred or thousand observations per series. However, in the last decade data sets containing tick-by-tick observations have become available. The studies of these data have turned up new and interesting facts about the pricing of assets. In this article we show that foreign exchange (FX) rate returns satisfy scaling with an exponent significantly different from that of a random walk. But what is more important, we also show that the conditionally exponential decay (CED) model can be used to solve a long standing problem in the analysis of intra-daily data, i.e. it can be used to identify the mathematical structure of the distributions of FX returns corresponding to the empirical scaling laws.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 2294.

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Date of creation: Jul 2002
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Handle: RePEc:pra:mprapa:2294

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Keywords: FX market; scaling law; volatility; CED model; high frequency data;

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References

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  1. Galluccio, S. & Caldarelli, G. & Marsili, M. & Zhang, Y.-C., 1997. "Scaling in currency exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 245(3), pages 423-436.
  2. Szymon Mercik & Rafal Weron, 1998. "Scaling in currency exchange: A Conditionally Exponential Decay approach," HSC Research Reports, Hugo Steinhaus Center, Wroclaw University of Technology HSC/98/02, Hugo Steinhaus Center, Wroclaw University of Technology.
  3. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, Springer, vol. 2(1), pages 41-68.
  4. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 47(2), pages 244-80, April.
  5. J-P. Bouchaud, 2001. "Power laws in economics and finance: some ideas from physics," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 1(1), pages 105-112.
  6. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, Econometric Society, vol. 41(1), pages 135-55, January.
  7. Aleksander Weron & Szymon Mercik & Rafal Weron, 1998. "Origins of the scaling behaviour in the dynamics of financial data," HSC Research Reports, Hugo Steinhaus Center, Wroclaw University of Technology HSC/98/01, Hugo Steinhaus Center, Wroclaw University of Technology.
  8. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, Elsevier, vol. 14(6), pages 1189-1208, December.
  9. Andersen, Torben G, 2000. "Some Reflections on Analysis of High-Frequency Data," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 18(2), pages 146-53, April.
  10. Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, Springer, vol. 1(2), pages 95-129.
  11. Hideaki Aoyama & Yuichi Nagahara & Mitsuhiro P. Okazaki & Wataru Souma & Hideki Takayasu & Misako Takayasu, 2000. "Pareto's Law for Income of Individuals and Debt of Bankrupt Companies," Papers cond-mat/0006038, arXiv.org.
  12. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
  13. Weron, Rafal & Weron, Karina & Weron, Aleksander, 1999. "A conditionally exponential decay approach to scaling in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 264(3), pages 551-561.
  14. Simon Hurst & Eckhard Platen & Svetlozar Rachev, 1997. "Subordinated Market Index Models: A Comparison," Asia-Pacific Financial Markets, Springer, Springer, vol. 4(2), pages 97-124, May.
  15. Sergio Da Silva & Raul Matsushita & Iram Gleria, 2002. "Scaling power laws in the Sao Paulo Stock Exchange," Economics Bulletin, AccessEcon, vol. 7(3), pages 1-12.
  16. Tucker, Alan L & Pond, Lallon, 1988. "The Probability Distribution of Foreign Exchange Price Changes: Tests of Candidate Processes," The Review of Economics and Statistics, MIT Press, vol. 70(4), pages 638-47, November.
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