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CATEGORIES:Statistics
SUMMARY:Limit theorems for nearly unstable Hawkes processe
s - Mathieu Rosenbaum\, University Pierre and Mari
e Curie (Paris 6)
DTSTART;TZID=Europe/London:20140425T160000
DTEND;TZID=Europe/London:20140425T170000
UID:TALK52095AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/52095
DESCRIPTION:Because of their tractability and their natural in
terpretations in term of market quantities\, Hawke
s processes are nowadays widely used in high frequ
ency finance. However\, in practice\, the statisti
cal estimation results seem to show that very ofte
n\, only nearly unstable Hawkes processes are able
to fit the data properly. By nearly unstable\, we
mean that the L1 norm of their kernel is close to
unity. We study in this work such processes for w
hich the stability condition is almost violated. O
ur main result states that after suitable rescalin
g\, they asymptotically\nbehave like integrated Co
x Ingersoll Ross models. Thus\, modeling financial
order flows as nearly unstable Hawkes processes m
ay be a good way to reproduce both their high and
low frequency stylized facts. We then extend this
result to the Hawkes based price model introduced
by Bacry et al. We show that under a similar criti
cality condition\, this process converges to a Hes
ton model. Again\, we recover well known stylized
facts of prices\, both at the microstructure level
and at the macroscopic scale.\n\nThis is joint wo
rk with Thibault Jaisson (Ecole Polytechnique Pari
s).
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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