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Drift in transcation-level asset price models

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Author Info

  • Wen Cao

    (IOMS - Information, Operations and Management Science - New York University)

  • Clifford Hurvich

    (IOMS - Information, Operations and Management Science - New York University)

  • Philippe Soulier

    ()
    (MODAL'X - Modélisation aléatoire de Paris X - Université Paris X - Paris Ouest Nanterre La Défense)

Abstract

We study the effect of drift in pure-jump transaction-level models for asset prices in continuous time, driven by point processes. The drift is assumed to arise from a nonzero mean in the efficient shock series. It follows that the drift is proportional to the driving point process itself, i.e. the cumulative number of transactions. This link reveals a mechanism by which properties of intertrade durations (such as heavy tails and long memory) can have a strong impact on properties of average returns, thereby potentially making it extremely difficult to determine growth rates. We focus on a basic univariate model for log price, coupled with general assumptions on durations that are satisfied by several existing flexible models, allowing for both long memory and heavy tails in durations. Under our pure-jump model, we obtain the limiting distribution for the suitably normalized log price. This limiting distribution need not be Gaussian, and may have either finite variance or infinite variance. We show that the drift can affect not only the limiting distribution for the normalized log price, but also the rate in the corresponding normalization. Therefore, the drift (or equivalently, the properties of durations) affects the rate of convergence of estimators of the growth rate, and can invalidate standard hypothesis tests for that growth rate. Our analysis also sheds some new light on two longstanding debates as to whether stock returns have long memory or infinite variance.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number hal-00756372.

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Date of creation: 21 Nov 2012
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Handle: RePEc:hal:wpaper:hal-00756372

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Related research

Keywords: Transaction-level asset prices modeling. Point processes. Heavy tails. Long memory.;

References

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  1. Hurvich, Clifford M. & Wang, Yi, 2010. "A Pure-Jump Transaction-Level Price Model Yielding Cointegration," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 539-558.
  2. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  3. Scholes, Myron & Williams, Joseph, 1977. "Estimating betas from nonsynchronous data," Journal of Financial Economics, Elsevier, vol. 5(3), pages 309-327, December.
  4. Hsieh, Meng-Chen & Hurvich, Clifford M. & Soulier, Philippe, 2007. "Asymptotics for duration-driven long range dependent processes," Journal of Econometrics, Elsevier, vol. 141(2), pages 913-949, December.
  5. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  6. Clive G. Bowsher, 2003. "Modelling Security Market Events in Continuous Time: Intensity Based, Multivariate Point Process Models," Economics Papers 2003-W03, Economics Group, Nuffield College, University of Oxford.
  7. E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 65-77, January.
  8. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  9. Fei Chen & Francis X. Diebold & Frank Schorfheide, 2012. "A Markov-Switching Multi-Fractal Inter-Trade Duration Model, with Application to U.S. Equities," PIER Working Paper Archive 12-020, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  10. repec:hal:wpaper:hal-00583372 is not listed on IDEAS
  11. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  12. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  13. Bauwens, Luc & Veredas, David, 2004. "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," Journal of Econometrics, Elsevier, vol. 119(2), pages 381-412, April.
  14. Deo, Rohit & Hurvich, Clifford M. & Soulier, Philippe & Wang, Yi, 2009. "Conditions For The Propagation Of Memory Parameter From Durations To Counts And Realized Volatility," Econometric Theory, Cambridge University Press, vol. 25(03), pages 764-792, June.
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