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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Stochastic dynamics of limit order books: a journe
y across time scales - Rama Cont (University of Ox
ford)
DTSTART;TZID=Europe/London:20240806T160000
DTEND;TZID=Europe/London:20240806T163000
UID:TALK218035AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/218035
DESCRIPTION:The intraday dynamics of electronic financial mark
ets is the outcome \; of a complex interplay b
etween buy and sell orders submitted across a wide
range of frequencies by various market participan
ts. The state of such a market may be represented
by the limit order book\, a \; multiclass queu
eing system indexed by positive integers (price le
vels)\, whose stochastic evolution summarizes the
dynamics of supply and demand. Given the very high
frequency of order arrivals\, heavy traffic limit
s and diffusion approximations provide relevant de
scriptions for price and order flow dynamics at va
rious time resolutions. The multiplicity of time s
cales at play and the availability of detailed dat
a down to microsecond \; level make limit orde
r book dynamics an interesting laboratory for asym
ptotic methods in queueing theory.\nOne approach i
s to describe the dynamics of the full limit order
book by a stochastic PDE\, for which different fo
rmulations \; have been proposed. We argue tha
t the &lsquo\;correct&rsquo\; limit is a spatially
inhomogeneous limit which leads to a &lsquo\;dege
nerate&rsquo\; stochastic moving -boundary problem
s with white noise perturbations on the boundary.\
nA more tractable approach is to zoom in on the &l
squo\;boundary layer&rsquo\; corresponding to the
queues with the best buy and sell prices (&lsquo\;
top&rsquo\; of the order book) and describe their
stochastic dynamics as a tandem queue model whose
state space is the positive quadrant. Depletion of
the buy and sell queues then lead to discontinuou
s stochastic reflection at the boundary\, and in t
he heavy traffic limit one retrieves a regulated B
rownian motion inside the quadrant with stochastic
discontinuous reflection on the boundary. Price d
ynamics is then described by a the difference of t
wo boundary occupation time processes.\nIf time pe
rmits we will also discuss a host of related open
problems relevant for applications.
LOCATION:External
CONTACT:
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