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SUMMARY:Stochastic dynamics of limit order books: a journey across time sc
 ales - Rama Cont (University of Oxford)
DTSTART:20240806T150000Z
DTEND:20240806T153000Z
UID:TALK218035@talks.cam.ac.uk
DESCRIPTION:The intraday dynamics of electronic financial markets is the o
 utcome&nbsp\; of a complex interplay between buy and sell orders submitted
  across a wide range of frequencies by various market participants. The st
 ate of such a market may be represented by the limit order book\, a&nbsp\;
  multiclass queueing system indexed by positive integers (price levels)\, 
 whose stochastic evolution summarizes the dynamics of supply and demand. G
 iven the very high frequency of order arrivals\, heavy traffic limits and 
 diffusion approximations provide relevant descriptions for price and order
  flow dynamics at various time resolutions. The multiplicity of time scale
 s at play and the availability of detailed data down to microsecond&nbsp\;
  level make limit order book dynamics an interesting laboratory for asympt
 otic methods in queueing theory.\nOne approach is to describe the dynamics
  of the full limit order book by a stochastic PDE\, for which different fo
 rmulations&nbsp\; have been proposed. We argue that the &lsquo\;correct&rs
 quo\; limit is a spatially inhomogeneous limit which leads to a &lsquo\;de
 generate&rsquo\; stochastic moving -boundary problems with white noise per
 turbations on the boundary.\nA more tractable approach is to zoom in on th
 e &lsquo\;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 disc
 ontinuous stochastic reflection at the boundary\, and in the heavy traffic
  limit one retrieves a regulated Brownian motion inside the quadrant with 
 stochastic discontinuous reflection on the boundary. Price dynamics is the
 n described by a the difference of two boundary occupation time processes.
 \nIf time permits we will also discuss a host of related open problems rel
 evant for applications.
LOCATION:External
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