Long-Time Behavior of a Hawkes Process--Based Limit Order Book

Frédéric Abergel and Aymen Jedidi
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Frédéric Abergel: FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec, MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris
Aymen Jedidi: FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec

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Abstract: Hawkes processes provide a natural framework to model dependencies between the intensities of point processes. In the context of order-driven financial markets, the relevance of such dependencies has been amply demonstrated from an empirical, as well as theoretical, standpoint. In this work, we build on previous empirical and numerical studies and introduce a mathematical model of limit order books based on Hawkes processes with exponential kernels. After proving a general stationarity result, we focus on the long-time behaviour of the limit order book and the corresponding dynamics of the suitably rescaled price. A formula for the asymptotic (in time) volatility of the price dynamics induced by that of the order book is obtained, involving the average of functions of the various order book events under the stationary distribution.

Date: 2015-11-05
New Economics Papers: this item is included in nep-mst
Note: View the original document on HAL open archive server: https://hal.science/hal-01121711v5
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Published in SIAM Journal on Financial Mathematics, 2015, 6 (1), pp.1026-1043. ⟨10.1137/15m1011469⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01121711

DOI: 10.1137/15m1011469

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