Clustering and Mean Reversion in a Hawkes Microstructure Model

Forthcoming The Journal of Futures Markets

31 Pages Posted: 22 Apr 2014 Last revised: 20 Jul 2015

See all articles by José Da Fonseca

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law

Riadh Zaatour

Ecole Centrale Paris

Date Written: July 20, 2015

Abstract

This paper provides explicit formulas for the first and second moments and the autocorrelation function of the number of jumps over a given interval for the multivariate Hawkes process. These computations are possible thanks to the affine property of this process. We unify the stock price models of Bacry et al. (2013a) and Da Fonseca and Zaatour (2013) both of them based on the Hawkes process, the first one having a mean reverting behaviour whilst the second one has a clustering behaviour, and build a model having these two properties. We compute various statistics as well as the diffusive limit for the stock price that determines the connection between the parameters driving the high frequency activity to the daily volatility. Lastly, the impulse function giving the impact on the stock price of a buy/sell trade is explicitly computed.

Keywords: Hawkes process, Clustering and Mean reversion, Volatility, Diffusive limit, Market Impact

JEL Classification: C13, C32, C58

Suggested Citation

Da Fonseca, José and Zaatour, Riadh, Clustering and Mean Reversion in a Hawkes Microstructure Model (July 20, 2015). Forthcoming The Journal of Futures Markets. Available at SSRN: https://ssrn.com/abstract=2427145 or http://dx.doi.org/10.2139/ssrn.2427145

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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