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SUMMARY:Limit theorems for nearly unstable Hawkes processes - Mathieu Rose
 nbaum\, University Pierre and Marie Curie (Paris 6)
DTSTART:20140425T150000Z
DTEND:20140425T160000Z
UID:TALK52095@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:Because of their tractability and their natural interpretation
 s in term of market quantities\, Hawkes processes are nowadays widely used
  in high frequency finance. However\, in practice\, the statistical estima
 tion results seem to show that very often\, only nearly unstable Hawkes pr
 ocesses are able to fit the data properly. By nearly unstable\, we mean th
 at the L1 norm of their kernel is close to unity. We study in this work su
 ch processes for which the stability condition is almost violated. Our mai
 n result states that after suitable rescaling\, they asymptotically\nbehav
 e like integrated Cox Ingersoll Ross models. Thus\, modeling financial ord
 er flows as nearly unstable Hawkes processes may be a good way to reproduc
 e both their high and low frequency stylized facts. We then extend this re
 sult to the Hawkes based price model introduced by Bacry et al. We show th
 at under a similar criticality condition\, this process converges to a Hes
 ton model. Again\, we recover well known stylized facts of prices\, both a
 t the microstructure level and at the macroscopic scale.\n\nThis is joint 
 work with Thibault Jaisson (Ecole Polytechnique Paris).
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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