A reduced form framework for modeling volatility of speculative prices based on realized variation measures

Torben G. Andersen, Tim Bollerslev, Xin Huang

Research output: Contribution to journalArticlepeer-review

128 Scopus citations


Building on realized variance and bipower variation measures constructed from high-frequency financial prices, we propose a simple reduced form framework for effectively incorporating intraday data into the modeling of daily return volatility. We decompose the total daily return variability into the continuous sample path variance, the variation arising from discontinuous jumps that occur during the trading day, as well as the overnight return variance. Our empirical results, based on long samples of high-frequency equity and bond futures returns, suggest that the dynamic dependencies in the daily continuous sample path variability are well described by an approximate long-memory HARGARCH model, while the overnight returns may be modeled by an augmented GARCH type structure. The dynamic dependencies in the non-parametrically identified significant jumps appear to be well described by the combination of an ACH model for the time-varying jump intensities coupled with a relatively simple log-linear structure for the jump sizes. Finally, we discuss how the resulting reduced form model structure for each of the three components may be used in the construction of out-of-sample forecasts for the total return volatility.

Original languageEnglish (US)
Pages (from-to)176-189
Number of pages14
JournalJournal of Econometrics
Issue number1
StatePublished - Jan 2011


  • Bipower variation
  • Hazard rates
  • Jumps
  • Overnight volatility
  • Realized variation
  • Stochastic volatility

ASJC Scopus subject areas

  • Economics and Econometrics


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