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Hawkes Process: Fast Calibration, Application to Trade Clustering and Diffusive Limit

42 Pages Posted: 15 Jul 2013 Last revised: 5 Aug 2013

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law

Riadh Zaatour

Ecole Centrale Paris

Date Written: August 4, 2013

Abstract

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

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

José Da Fonseca (Contact Author)

Auckland University of Technology - Faculty of Business & Law ( email )

3 Wakefield Street
Private Bag 92006
Auckland Central 1020
New Zealand
64 9 921 9999 5063 (Phone)

Riadh Zaatour

Ecole Centrale Paris ( email )

2 Avenue Sully Prudhomme
92290
Châtenay-Malabry
France

HOME PAGE: http://fiquant.mas.ecp.fr/

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