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Intraday volatility and scaling in high frequency foreign exchange markets

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  • Seemann, Lars
  • McCauley, Joseph L.
  • Gunaratne, Gemunu H.

Abstract

Recent reports suggest that the stochastic process underlying financial time series is nonstationary with nonstationary increments. Therefore, time averaging techniques through sliding intervals are inappropriate and ensemble methods have been proposed. Using daily ensemble averages we analyze two different measures of intraday volatility, trading frequency and the mean square fluctuation of increments for the three most active FX markets; we find that both measures indicate that the underlying stochastic dynamics exhibits nonstationary increments. We show that the two volatility measures are equivalent. In each market we find three time intervals during the day where the mean square fluctuation of increments can be fit by power law scaling in time. The scaling indices in the intervals are different, but independent of the FX market under study. We also find that the fluctuations in return in these intervals lie on exponential distributions.

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  • Seemann, Lars & McCauley, Joseph L. & Gunaratne, Gemunu H., 2011. "Intraday volatility and scaling in high frequency foreign exchange markets," International Review of Financial Analysis, Elsevier, vol. 20(3), pages 121-126, June.
    • Handle: RePEc:eee:finana:v:20:y:2011:i:3:p:121-126
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    as
    1. Joseph L. McCauley, 2008. "Time vs. Ensemble Averages for Nonstationary Time Series," Papers 0804.0902, arXiv.org.
    2. Gabriele Galati & Alexandra Heath, 2007. "What drives the growth in FX activity? Interpreting the 2007 triennial survey," BIS Quarterly Review, Bank for International Settlements, December.
    3. Baviera, Roberto & Pasquini, Michele & Serva, Maurizio & Vergni, Davide & Vulpiani, Angelo, 2001. "Correlations and multi-affinity in high frequency financial datasets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(3), pages 551-557.
    4. M. F. M. Osborne, 1959. "Brownian Motion in the Stock Market," Operations Research, INFORMS, vol. 7(2), pages 145-173, April.
    5. Brownlees, C.T. & Gallo, G.M., 2006. "Financial econometric analysis at ultra-high frequency: Data handling concerns," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2232-2245, December.
    6. Benoit Mandelbrot & Howard M. Taylor, 1967. "On the Distribution of Stock Price Differences," Operations Research, INFORMS, vol. 15(6), pages 1057-1062, December.
    7. Bassler, Kevin E. & Gunaratne, Gemunu H. & McCauley, Joseph L., 2008. "Empirically based modeling in financial economics and beyond, and spurious stylized facts," International Review of Financial Analysis, Elsevier, vol. 17(5), pages 767-783, December.
    8. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, September.
    9. 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, vol. 1(2), pages 95-129.
    10. Bassler, Kevin E. & Gunaratne, Gemunu H. & McCauley, Joseph L., 2006. "Markov processes, Hurst exponents, and nonlinear diffusion equations: With application to finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 343-353.
    11. Gunaratne, Gemunu H. & Nicol, Matthew & Seemann, Lars & Török, Andrei, 2009. "Clustering of volatility in variable diffusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(20), pages 4424-4430.
    12. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    13. Gopikrishnan, P & Plerou, V & Liu, Y & Amaral, L.A.N & Gabaix, X & Stanley, H.E, 2000. "Scaling and correlation in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 362-373.
    14. Dacorogna, Michael M. & Muller, Ulrich A. & Nagler, Robert J. & Olsen, Richard B. & Pictet, Olivier V., 1993. "A geographical model for the daily and weekly seasonal volatility in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 12(4), pages 413-438, August.
    15. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
    16. Galluccio, S. & Caldarelli, G. & Marsili, M. & Zhang, Y.-C., 1997. "Scaling in currency exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 423-436.
    17. Silva, A. Christian & Yakovenko, Victor M., 2007. "Stochastic volatility of financial markets as the fluctuating rate of trading: An empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 278-285.
    18. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    19. 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, vol. 14(6), pages 1189-1208, December.
    20. Jim Griffin & Roel Oomen, 2008. "Sampling Returns for Realized Variance Calculations: Tick Time or Transaction Time?," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 230-253.
    21. Thierry Ané & Hélyette Geman, 2000. "Order Flow, Transaction Clock, and Normality of Asset Returns," Journal of Finance, American Finance Association, vol. 55(5), pages 2259-2284, October.
    22. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    23. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
    24. Oomen, Roel C.A., 2006. "Properties of Realized Variance Under Alternative Sampling Schemes," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 219-237, April.
    25. McCauley,Joseph L., 2009. "Dynamics of Markets," Cambridge Books, Cambridge University Press, number 9780521429627, September.
    26. Xu, Zhaoxia & Gençay, Ramazan, 2003. "Scaling, self-similarity and multifractality in FX markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 578-590.
    27. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    28. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    29. Silva, A. Christian & Prange, Richard E. & Yakovenko, Victor M., 2004. "Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 227-235.
    30. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    31. Kevin E. Bassler & Gemunu H. Gunaratne & Joseph L. McCauley, 2006. "Markov Processes, Hurst Exponents, and Nonlinear Diffusion Equations with application to finance," Papers cond-mat/0602316, arXiv.org.
    32. McCauley, Joseph L., 2008. "Time vs. ensemble averages for nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5518-5522.
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    6. F. Baldovin & F. Camana & M. Caporin & M. Caraglio & A.L. Stella, 2015. "Ensemble properties of high-frequency data and intraday trading rules," Quantitative Finance, Taylor & Francis Journals, vol. 15(2), pages 231-245, February.
    7. Baklaci, Hasan Fehmi & Aydoğan, Berna & Yelkenci, Tezer, 2020. "Impact of stock market trading on currency market volatility spillovers," Research in International Business and Finance, Elsevier, vol. 52(C).
    8. Michael Frömmel & Eyup Kadioglu, 2023. "Impact of trading hours extensions on foreign exchange volatility: intraday evidence from the Moscow exchange," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-23, December.
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    10. v{S}tefan Ly'ocsa & Tom'av{s} Pl'ihal, 2022. "Russia's Ruble during the onset of the Russian invasion of Ukraine in early 2022: The role of implied volatility and attention," Papers 2205.09179, arXiv.org.
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