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Instantaneous Volatility Seasonality of High-Frequency Markets in Directional-Change Intrinsic Time

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  • Vladimir Petrov

    (Department of Banking and Finance, University of Zurich, Plattenstrasse 14, 8032 Zurich, Switzerland
    Current address: Department of Banking and Finance, University of Zurich, Plattenstrasse 14, 8032 Zurich, Switzerland.)

  • Anton Golub

    (Flov Technologies AG, Gotthardstrasse 26, 6300 Zug, Switzerland)

  • Richard Olsen

    (Lykke Corp., Alpenstrasse 9, 6300 Zug, Switzerland)

Abstract

We propose a novel intraday instantaneous volatility measure which utilises sequences of drawdowns and drawups non-equidistantly spaced in physical time as indicators of high-frequency activity of financial markets. The sequences are re-expressed in terms of directional-change intrinsic time which ticks only when the price curve changes the direction of its trend by a given relative value. We employ the proposed measure to uncover weekly volatility seasonality patterns of three Forex and one Bitcoin exchange rates, as well as a stock market index. We demonstrate the long memory of instantaneous volatility computed in directional-change intrinsic time. The provided volatility estimation method can be adapted as a universal multiscale risk-management tool independent of the discreteness and the type of analysed high-frequency data.

Suggested Citation

  • Vladimir Petrov & Anton Golub & Richard Olsen, 2019. "Instantaneous Volatility Seasonality of High-Frequency Markets in Directional-Change Intrinsic Time," JRFM, MDPI, vol. 12(2), pages 1-31, April.
    • Handle: RePEc:gam:jjrfmx:v:12:y:2019:i:2:p:54-:d:219095
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    as
    1. Angelos Dassios & Jia Wei Lim, 2018. "An Efficient Algorithm for Simulating the Drawdown Stopping Time and the Running Maximum of a Brownian Motion," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 189-204, March.
    2. Alexei Chekhlov & Stanislav Uryasev & Michael Zabarankin, 2005. "Drawdown Measure In Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 13-58.
    3. M. F. M. Osborne, 1959. "Brownian Motion in the Stock Market," Operations Research, INFORMS, vol. 7(2), pages 145-173, April.
    4. Olympia Hadjiliadis & Jan Vecer, 2006. "Drawdowns preceding rallies in the Brownian motion model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 403-409.
    5. Takuya Shintate & Lukáš Pichl, 2019. "Trend Prediction Classification for High Frequency Bitcoin Time Series with Deep Learning," JRFM, MDPI, vol. 12(1), pages 1-15, January.
    6. Ito, Takatoshi & Hashimoto, Yuko, 2006. "Intraday seasonality in activities of the foreign exchange markets: Evidence from the electronic broking system," Journal of the Japanese and International Economies, Elsevier, vol. 20(4), pages 637-664, December.
    7. 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.
    8. Rozeff, Michael S. & Kinney, William Jr., 1976. "Capital market seasonality: The case of stock returns," Journal of Financial Economics, Elsevier, vol. 3(4), pages 379-402, October.
    9. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
    10. Hartmann, Philipp, 1999. "Trading volumes and transaction costs in the foreign exchange market: Evidence from daily dollar-yen spot data," Journal of Banking & Finance, Elsevier, vol. 23(5), pages 801-824, May.
    11. Mustafa Gultekin & Bulent Gultekin, "undated". "Stock Market Seasonality: Internal Evidence," Rodney L. White Center for Financial Research Working Papers 17-83, Wharton School Rodney L. White Center for Financial Research.
    12. Campbell, John Y. & Giglio, Stefano & Polk, Christopher & Turley, Robert, 2018. "An intertemporal CAPM with stochastic volatility," Journal of Financial Economics, Elsevier, vol. 128(2), pages 207-233.
    13. J. B. Glattfelder & A. Dupuis & R. B. Olsen, 2010. "Patterns in high-frequency FX data: discovery of 12 empirical scaling laws," Quantitative Finance, Taylor & Francis Journals, vol. 11(4), pages 599-614.
    14. Eross, Andrea & McGroarty, Frank & Urquhart, Andrew & Wolfe, Simon, 2019. "The intraday dynamics of bitcoin," Research in International Business and Finance, Elsevier, vol. 49(C), pages 71-81.
    15. Jondeau, Eric & Rockinger, Michael, 2003. "Testing for differences in the tails of stock-market returns," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 559-581, December.
    16. Pospisil, Libor & Vecer, Jan & Hadjiliadis, Olympia, 2009. "Formulas for stopped diffusion processes with stopping times based on drawdowns and drawups," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2563-2578, August.
    17. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    18. 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.
    19. John Cotter, 2005. "Tail behaviour of the euro," Applied Economics, Taylor & Francis Journals, vol. 37(7), pages 827-840.
    20. Gultekin, Mustafa N. & Gultekin, N. Bulent, 1983. "Stock market seasonality : International Evidence," Journal of Financial Economics, Elsevier, vol. 12(4), pages 469-481, December.
    21. Gottlieb, Gary & Kalay, Avner, 1985. "Implications of the Discreteness of Observed Stock Prices," Journal of Finance, American Finance Association, vol. 40(1), pages 135-153, March.
    22. French, Kenneth R. & Roll, Richard, 1986. "Stock return variances : The arrival of information and the reaction of traders," Journal of Financial Economics, Elsevier, vol. 17(1), pages 5-26, September.
    23. Lukas Menkhoff & Lucio Sarno & Maik Schmeling & Andreas Schrimpf, 2012. "Carry Trades and Global Foreign Exchange Volatility," Journal of Finance, American Finance Association, vol. 67(2), pages 681-718, April.
    24. Seif, Mostafa & Docherty, Paul & Shamsuddin, Abul, 2017. "Seasonal anomalies in advanced emerging stock markets," The Quarterly Review of Economics and Finance, Elsevier, vol. 66(C), pages 169-181.
    25. 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.
    26. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    27. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
    28. Bessembinder, Hendrik, 1994. "Bid-ask spreads in the interbank foreign exchange markets," Journal of Financial Economics, Elsevier, vol. 35(3), pages 317-348, June.
    29. Chstoph Bandt & Faten Shiha, 2007. "Order Patterns in Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(5), pages 646-665, September.
    30. Bollerslev, Tim & Melvin, Michael, 1994. "Bid--ask spreads and volatility in the foreign exchange market : An empirical analysis," Journal of International Economics, Elsevier, vol. 36(3-4), pages 355-372, May.
    31. Lily Fang & Chunmei Lin & Yuping Shao, 2018. "School Holidays and Stock Market Seasonality," Financial Management, Financial Management Association International, vol. 47(1), pages 131-157, March.
    32. J. L. Kelly Jr., 2011. "A New Interpretation of Information Rate," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 3, pages 25-34, World Scientific Publishing Co. Pte. Ltd..
    33. Anton Golub & Gregor Chliamovitch & Alexandre Dupuis & Bastien Chopard, 2014. "Multi-scale Representation of High Frequency Market Liquidity," Papers 1402.2198, arXiv.org.
    34. Keim, Donald B., 1983. "Size-related anomalies and stock return seasonality : Further empirical evidence," Journal of Financial Economics, Elsevier, vol. 12(1), pages 13-32, June.
    35. Ruiping Liu & Zhichao Shao & Guodong Wei & Wei Wang, 2017. "GARCH Model With Fat-Tailed Distributions and Bitcoin Exchange Rate Returns," Journal of Accounting, Business and Finance Research, Scientific Publishing Institute, vol. 1(1), pages 71-75.
    36. De Bondt, Werner F M & Thaler, Richard H, 1987. "Further Evidence on Investor Overreaction and Stock Market Seasonalit y," Journal of Finance, American Finance Association, vol. 42(3), pages 557-581, July.
    37. Dyhrberg, Anne Haubo, 2016. "Bitcoin, gold and the dollar – A GARCH volatility analysis," Finance Research Letters, Elsevier, vol. 16(C), pages 85-92.
    38. Hasbrouck, Joel, 2018. "High-Frequency Quoting: Short-Term Volatility in Bids and Offers," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 53(2), pages 613-641, April.
    39. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    40. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    41. Schuhmacher, Frank & Eling, Martin, 2011. "Sufficient conditions for expected utility to imply drawdown-based performance rankings," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2311-2318, September.
    42. Begušić, Stjepan & Kostanjčar, Zvonko & Eugene Stanley, H. & Podobnik, Boris, 2018. "Scaling properties of extreme price fluctuations in Bitcoin markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 400-406.
    43. 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.
    44. repec:bla:jfinan:v:43:y:1988:i:2:p:451-66 is not listed on IDEAS
    45. Hongzhong Zhang & Olympia Hadjiliadis, 2012. "Drawdowns and the Speed of Market Crash," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 739-752, September.
    46. Bollerslev, Tim & Domowitz, Ian, 1993. "Trading Patterns and Prices in the Interbank Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 48(4), pages 1421-1443, September.
    47. 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.
    48. Zarowin, Paul, 1990. "Size, Seasonality, and Stock Market Overreaction," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(1), pages 113-125, March.
    49. Dyhrberg, Anne H. & Foley, Sean & Svec, Jiri, 2018. "How investible is Bitcoin? Analyzing the liquidity and transaction costs of Bitcoin markets," Economics Letters, Elsevier, vol. 171(C), pages 140-143.
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    Cited by:

    1. Lars Stentoft, 2020. "Computational Finance," JRFM, MDPI, vol. 13(7), pages 1-4, July.
    2. Shengnan Li & Edward P. K. Tsang & John O'Hara, 2022. "Measuring relative volatility in high‐frequency data under the directional change approach," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 29(2), pages 86-102, April.
    3. James B. Glattfelder & Anton Golub, 2022. "Bridging the Gap: Decoding the Intrinsic Nature of Time in Market Data," Papers 2204.02682, arXiv.org.
    4. James B. Glattfelder & Richard B. Olsen, 2024. "The Theory of Intrinsic Time: A Primer," Papers 2406.07354, arXiv.org.

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