IDEAS home Printed from https://ideas.repec.org/a/wsi/afexxx/v10y2015i02ns2010495215500116.html
   My bibliography  Save this article

Construction Of Models For Bounded Price Processes: The Case Of The Hkd Exchange Rate

Author

Listed:
  • HONG BEN YEE

    (Department of Mathematics Statistics, Curtin University, GPO Box U1987, Perth, Western Australia 6845, Australia)

  • NIKOLAI DOKUCHAEV

    (Department of Mathematics Statistics, Curtin University, GPO Box U1987, Perth, Western Australia 6845, Australia)

Abstract

This paper discusses construction of evolution models for financial time series evolving within a given interval. We calibrated a model for the case of the USD/HKD exchange rate after the separation of strong and weak side convertibility undertakings, in which the rate is confined to a specified corridor. This process represents an interesting example of a tradable bounded process. A one-dimensional (1D) model was able to replicate the bounded distribution of the process, but a two-dimensional (2D) model better captured dynamics as measured by the volatility without losing features of the 1D model. We briefly consider the ergodic properties of these models.

Suggested Citation

  • Hong Ben Yee & Nikolai Dokuchaev, 2015. "Construction Of Models For Bounded Price Processes: The Case Of The Hkd Exchange Rate," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 1-23, December.
    • Handle: RePEc:wsi:afexxx:v:10:y:2015:i:02:n:s2010495215500116
    DOI: 10.1142/S2010495215500116
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S2010495215500116
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S2010495215500116?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nicolau, João, 2002. "Stationary Processes That Look Like Random Walks— The Bounded Random Walk Process In Discrete And Continuous Time," Econometric Theory, Cambridge University Press, vol. 18(1), pages 99-118, February.
    2. 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, vol. 47(2), pages 244-280, April.
    3. McFarland, James W & Pettit, R Richardson & Sung, Sam K, 1982. "The Distribution of Foreign Exchange Price Changes: Trading Day Effects and Risk Measurement," Journal of Finance, American Finance Association, vol. 37(3), pages 693-715, June.
    4. Jeffrey A. Frankel, 1999. "No Single Currency Regime is Right for All Countries or At All Times," NBER Working Papers 7338, National Bureau of Economic Research, Inc.
    5. 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.
    6. Baillie, Richard T & Bollerslev, Tim, 2002. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 60-68, January.
    7. Carcano, G. & Falbo, P. & Stefani, S., 2005. "Speculative trading in mean reverting markets," European Journal of Operational Research, Elsevier, vol. 163(1), pages 132-144, May.
    8. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 669-682.
    9. Nikolai Dokuchaev, 2014. "Volatility estimation from short time series of stock prices," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 373-384, June.
    10. Nikolai Dokuchaev, 2007. "Mean-Reverting Market Model: Speculative Opportunities and Non-Arbitrage," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 319-337.
    11. Cho-Hoi Hui & Tom Fong, 2007. "Is the Hong Kong Dollar Exchange Rate "Bounded" in the Convertibility Zone?," Working Papers 0713, Hong Kong Monetary Authority.
    12. 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.
    13. Hsieh, David A., 1988. "The statistical properties of daily foreign exchange rates: 1974-1983," Journal of International Economics, Elsevier, vol. 24(1-2), pages 129-145, February.
    14. 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.
    15. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    16. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    2. Mondher Bellalah & Marc Lavielle, 2002. "A Decomposition of Empirical Distributions with Applications to the Valuation of Derivative Assets," Multinational Finance Journal, Multinational Finance Journal, vol. 6(2), pages 99-130, June.
    3. repec:adr:anecst:y:1991:i:24:p:01 is not listed on IDEAS
    4. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    5. Muneer Shaik & S. Maheswaran, 2019. "Robust Volatility Estimation with and Without the Drift Parameter," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(1), pages 57-91, March.
    6. Ghose, Devajyoti & Kroner, Kenneth F., 1995. "The relationship between GARCH and symmetric stable processes: Finding the source of fat tails in financial data," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 225-251, September.
    7. Karuppiah, Jeyanthi & Los, Cornelis A., 2005. "Wavelet multiresolution analysis of high-frequency Asian FX rates, Summer 1997," International Review of Financial Analysis, Elsevier, vol. 14(2), pages 211-246.
    8. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    9. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    10. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    11. Dubovikov, M.M & Starchenko, N.V & Dubovikov, M.S, 2004. "Dimension of the minimal cover and fractal analysis of time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 339(3), pages 591-608.
    12. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    13. Seemann, Lars & Hua, Jia-Chen & McCauley, Joseph L. & Gunaratne, Gemunu H., 2012. "Ensemble vs. time averages in financial time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6024-6032.
    14. Hua, Jia-Chen & Chen, Lijian & Falcon, Liberty & McCauley, Joseph L. & Gunaratne, Gemunu H., 2015. "Variable diffusion in stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 221-233.
    15. Tim Bollerslev & Ray Y. Chou & Narayanan Jayaraman & Kenneth F. Kroner - L, 1991. "es modéles ARCH en finance : un point sur la théorie et les résultats empiriques," Annals of Economics and Statistics, GENES, issue 24, pages 1-59.
    16. Carol Alexander & Sujit Narayanan, 2001. "Option Pricing with Normal Mixture Returns: Modelling Excess Kurtosis and Uncertanity in Volatility," ICMA Centre Discussion Papers in Finance icma-dp2001-10, Henley Business School, University of Reading, revised Dec 2001.
    17. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    18. Steven Kou, 2000. "A Jump Diffusion Model for Option Pricing with Three Properties: Leptokurtic Feature, Volatility Smile, and Analytical Tractability," Econometric Society World Congress 2000 Contributed Papers 0062, Econometric Society.
    19. Deniz Erer, 2023. "The Impact of News Related Covid-19 on Exchange Rate Volatility:A New Evidence From Generalized Autoregressive Score Model," EKOIST Journal of Econometrics and Statistics, Istanbul University, Faculty of Economics, vol. 0(38), pages 105-126, June.
    20. Mercik, Szymon & Weron, Rafal, 2002. "Origins of scaling in FX markets," MPRA Paper 2294, University Library of Munich, Germany.
    21. Suárez-García, Pablo & Gómez-Ullate, David, 2013. "Scaling, stability and distribution of the high-frequency returns of the Ibex35 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1409-1417.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:afexxx:v:10:y:2015:i:02:n:s2010495215500116. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/afe/afe.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.