Modeling Ultra-High-Frequency Data: The S&P 500 Index Future

  • Marco Minozzo
  • Silvia Centanni
Conference paper


In recent years, marked point processes have found a natural application in the modeling of ultra-high-frequency financial data. The use of these processes does not require the integration of the data which is usually needed by other modeling approaches. Two main classes of marked point processes have so far been proposed to model financial data: the class of the autoregressive conditional duration models of Engle and Rüssel and the broad class of doubly stochastic Poisson processes with marks. In this paper, we show how to model an ultra-high-frequency data set relative to the prices of the future on the S&P 500 index using a particular class of doubly stochastic Poisson process. Our models allow a natural interpretation of the underlying intensity in terms of news reaching the market and does not require the use of ad hoc methods to treat the seasonalities. Filtering and estimation are carried out by Monte Carlo expectation maximization and reversible jump Markov chain Monte Carlo algorithms.

Key words

Cox process Marked point process Monte Carlo expectation maximization Reversible jump Markov chain Monte Carlo Shot noise process Tick by tick data 


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  1. [AB98]
    Andersen, T., Bollerslev, T.: Deutsche Mark-Dollar volatility: intraday activity patterns, macroeconomic announcements, and longer run dependencies. The Journal of Finance, 53, 219–265 (1998)CrossRefGoogle Scholar
  2. [BS01]
    Barndorff-Nielsen, O. E., Shephard, N.: Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics (with discussion). Journal of the Royal Statistical Society, Series B, 63, 167–241 (2001)CrossRefGoogle Scholar
  3. [CM06a]
    Centanni, S., Minozzo, M.: Estimation and filtering by reversible jump MCMC for a doubly stochastic Poisson model for ultra-high-frequency financial data. Statistical Modelling, 6, 97–118 (2006)CrossRefGoogle Scholar
  4. [CM06b]
    Centanni, S., Minozzo, M.: A Monte Carlo approach to filtering for a class of marked doubly stochastic Poisson processes. Journal of the American Statistical Association, 101, 1582–1597 (2006)CrossRefGoogle Scholar
  5. [CI80]
    Cox, D. R., Isham, V.: Point Processes. Chapman and Hall, London (1980)Google Scholar
  6. [ER98]
    Engle, R. F., Rüssel, J.R.: Autoregressive conditional duration: A new model for irregularly spaced transaction data. Econometrica, 66, 1127–1162 (1998)CrossRefGoogle Scholar
  7. [FM03]
    Fort, G., Moulines, E.: Convergence of the Monte Carlo expectation maximization for curved exponential families. The Annals of Statistics, 31, 1220–1259 (2003)CrossRefGoogle Scholar
  8. [GDD99]
    Guillaume, D.M., Dacorogna, M.M., Davé, R.R., Müller, U.A., Olsen, R.B., Pictet, O. V.: From the bird’s eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets. Finance and Stochastics, 1, 95–129 (1999)CrossRefGoogle Scholar
  9. [KLP04]
    Kalev, P. S., Liu, W. M., Pham, P. K., Jarnecic, E.: Public information arrival and volatility of intraday stock returns. Journal of Banking & Finance, 28, 1441–1467 (2004)CrossRefGoogle Scholar
  10. [P06]
    Peters, R.T.: Shocks in the S&P 500. Working paper, University of Amsterdam (2006)Google Scholar
  11. [PR85]
    Pierce, D.K., Roley, V. V.: Stock prices and economics news. Journal of Business, 58, 49–67 (1985)CrossRefGoogle Scholar
  12. [RPD04]
    Roberts, G.O., Papaspiliopoulos, O., Dellaportas, P.: Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes. Journal of the Royal Statistical Society, Series B, 66, 369–393 (2004)CrossRefGoogle Scholar
  13. [RS00]
    Rydberg, T. H., Shephard, N.: A modelling framework for the prices and times of trades made on the New York stock exchange. In: Fitzgerald, W.J., Smith, R.L., Waiden, A. T., Young, P. C. (eds) Nonlinear and Nonstationary Signal Processing, pp. 217–246 (2000)Google Scholar

Copyright information

© Springer, Milan 2008

Authors and Affiliations

  • Marco Minozzo
    • 1
  • Silvia Centanni
    • 2
  1. 1.University of PerugiaItaly
  2. 2.University of VeronaItaly

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