42 Pages Posted: 15 Jul 2013 Last revised: 5 Aug 2013
Date Written: August 4, 2013
This paper provides explicit formulas for the moments and the autocorrelation function of the number of jumps over a given interval for the Hawkes process. These computations are possible thanks to the affine property of this process. Using these quantities an implementation of the method of moments for parameter estimation that leads to an fast optimization algorithm is developed. The estimation strategy is applied to trade arrival times for major stocks that show a clustering behaviour, a feature the Hawkes process can effectively handle. As the calibration is fast, the estimation is rolled to determine the stability of the estimated parameters. Lastly, the analytical results enable the computation of the diffusive limit in a simple model for the price evolution based on the Hawkes process. It determines the connection between the parameters driving the high frequency activity to the daily volatility.
Keywords: Hawkes process, calibration, high-frequency data, trade clustering, diffusive limit
JEL Classification: C13, C32, C58
Suggested Citation: Suggested Citation
Da Fonseca, José and Zaatour, Riadh, Hawkes Process: Fast Calibration, Application to Trade Clustering and Diffusive Limit (August 4, 2013). Available at SSRN: https://ssrn.com/abstract=2294112 or http://dx.doi.org/10.2139/ssrn.2294112
By Jim Gatheral