Long-Time Behavior of a Hawkes Process--Based Limit Order Book
Résumé
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.
Origine : Fichiers produits par l'(les) auteur(s)
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