Application of Hawkes Volatility in the Observation of Filtered High-Frequency Price Process in Tick Structures

The Hawkes model is suitable for describing self and mutually exciting random events. In addition, the exponential decay in the Hawkes process allows us to calculate the moment properties of the model. However, owing to the complexity of the model and formula, few studies have examined the Hawkes volatility. In this study, we derive a variance formula that is directly applicable under the general settings of both unmarked and marked Hawkes models for tick-level price dynamics. In the marked model, the linear impact function and possible dependency between the marks and underlying processes are considered. The Hawkes volatility is applied to the mid-price process filtered at 0.1-s intervals to show reliable results. Furthermore, intraday estimation is expected to widely utilized in real-time risk management. We also note the increasing predictive power of the intraday Hawkes volatility over time and examine the relationship between futures and stock volatilities.