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Trading Patterns, Time Deformation and Stochastic Volatility in Foreign Exchange Markets

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Author Info
Eric Ghysels ()
Christian Gouriéroux
Joanna Jasiak

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Abstract

Globalization of trading in foreign exchange markets is a principal source of the daily and weekly seasonability in market volatility. One way to model such phenomena is to adopt a framework where market volatility is tied to the intensity of (world) trading through a subordinated stochastic process representation. In this paper we combine elements from Clark (1973), Dacorogna et al. (1993) and Ghysels and Jasiak (1994), and present a stochastic volatility model for foreign exchange markets with time deformation. The time deformation is based on daily patterns of arrivals of quotes and bid-ask spreads as well as returns. For empirical estimation we use the QMLE algorithm of Harvey et al. (1994), adopted by Ghysels and Jasiak for time deformed processes, and applied to the Olsen and Associates high frequency data set.

La globalisation des échanges sur le marché mondial des taux de change est une des sources principales des effets saisonniers journaliers et hebdomadaires dans la volatilité des prix. Une façon de modéliser ces phénomènes consiste à utiliser la spécification d'un processus subordonné pour formaliser la relation entre la volatilité et l'intensité des échanges. Cet article, fondé sur les idées de Clark (1973), Dacorogna et al. (1993) et Ghysels et Jasiak (1994), présente un modèle de volatilité stochastique avec la déformation du temps pour les séries des taux de change. La déformation du temps est déterminée par la dynamique du flux des cotations à travers la journée, les fourchettes de prix passées ainsi que les rendements antérieurs. Dans la partie empirique, nous appliquons ce modèle aux données de haute fréquence de Olsen and Associates. La méthode d'estimation que nous avons employée est le Quasi-Maximum de Vraisemblance proposé par Harvey et Stock, adapté par Ghysels et Jasiak aux processus déformés du temps.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 95s-42.

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Date of creation: 01 Oct 1995
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Handle: RePEc:cir:cirwor:95s-42

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  4. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January. [Downloadable!] (restricted)
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  10. 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. [Downloadable!] (restricted)
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  12. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June. [Downloadable!] (restricted)
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  22. Bollerslev, T. & Ghysels, E., 1994. "Periodic Autoregressive Conditional Heteroskedasticity," Cahiers de recherche 9408, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  28. Karpoff, Jonathan M., 1987. "The Relation between Price Changes and Trading Volume: A Survey," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(01), pages 109-126, March. [Downloadable!]
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  2. Robert F. Engle, 1996. "The Econometrics of Ultra-High Frequency Data," NBER Working Papers 5816, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  3. Torben G. Andersen & Tim Bollerslev, 1996. "Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," NBER Working Papers 5752, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  4. Jérôme Fillol, 2003. "Multifractality: Theory and Evidence an Application to the French Stock Market," Economics Bulletin, Economics Bulletin, vol. 3(31), pages 1-12. [Downloadable!]
  5. Eric Ghysels & Christian Gouriéroux & Joanna Jasiak, 1995. "Market Time and Asset Price Movements Theory and Estimation," CIRANO Working Papers 95s-32, CIRANO. [Downloadable!]
    Other versions:
  6. Adlai Fisher & Laurent Calvet & Benoit Mandelbrot, 1997. "Multifractality of Deutschemark/US Dollar Exchange Rates," Cowles Foundation Discussion Papers 1166, Cowles Foundation, Yale University. [Downloadable!]
  7. Eric Ghysels & Joanna Jasiak, 1997. "GARCH for Irregularly Spaced Data: The ACD-GARCH Model," CIRANO Working Papers 97s-06, CIRANO. [Downloadable!]
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