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Keywords:

  • Kalman filter;
  • Leverage;
  • Lévy process;
  • Power variation;
  • Quadratic variation;
  • Quarticity;
  • Realized volatility;
  • Stochastic volatility;
  • Subordination;
  • Superposition

Summary. The availability of intraday data on the prices of speculative assets means that we can use quadratic variation-like measures of activity in financial markets, called realized volatility, to study the stochastic properties of returns. Here, under the assumption of a rather general stochastic volatility model, we derive the moments and the asymptotic distribution of the realized volatility error—the difference between realized volatility and the discretized integrated volatility (which we call actual volatility). These properties can be used to allow us to estimate the parameters of stochastic volatility models without recourse to the use of simulation-intensive methods.