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Intraday Stochastic Volatility in Discrete Price Changes: the Dynamic Skellam Model

Author

Listed:
  • Siem Jan Koopman

    (VU University Amsterdam)

  • Rutger Lit

    (VU University Amsterdam)

  • Andre Lucas

    (VU University Amsterdam)

Abstract

We introduce a dynamic Skellam model that measures stochastic volatility from high-frequency tick-by-tick discrete stock price changes. The likelihood function for our model is analytically intractable and requires Monte Carlo integration methods for its numerical evaluation. The proposed methodology is applied to tick-by-tick data of four stocks traded on the New York Stock Exchange. We require fast simulation methods for likelihood evaluation since the number of observations per series per day varies from 1000 to 10,000. Complexities in the intraday dynamics of volatility and in the frequency of trades without price impact require further non-trivial adjustments to the dynamic Skellam model. In-sample residual diagnostics and goodness-of-fit statistics show that the final model provides a good fit to the data. An extensive forecasting study of intraday volatility shows that the dynamic modified Skellam model provides accurate forecasts compared to alternative modeling approaches.

Suggested Citation

  • Siem Jan Koopman & Rutger Lit & Andre Lucas, 2015. "Intraday Stochastic Volatility in Discrete Price Changes: the Dynamic Skellam Model," Tinbergen Institute Discussion Papers 15-076/IV/DSF94, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20150076
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Leopoldo Catania & Roberto Di Mari & Paolo Santucci de Magistris, 2019. "Dynamic discrete mixtures for high frequency prices," Discussion Papers 19/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    2. repec:eee:intfor:v:35:y:2019:i:2:p:797-809 is not listed on IDEAS
    3. Koopman, Siem Jan & Lit, Rutger, 2019. "Forecasting football match results in national league competitions using score-driven time series models," International Journal of Forecasting, Elsevier, vol. 35(2), pages 797-809.

    More about this item

    Keywords

    non-Gaussian time series models; volatility models; importance sampling; numerical integration; high-frequency data; discrete price changes.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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