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Mathematical Finance and Probability Seminars

ENDOGENOUS FORMATION OF LIMIT ORDER BOOKS: DYNAMICS BETWEEN TRADES

Location:  Hill 705
Date & time: Tuesday, 18 October 2016 at 11:45AM -

Sergey Nadtochiy, University of Michigan

"ENDOGENOUS FORMATION OF LIMIT ORDER BOOKS: DYNAMICS BETWEEN TRADES"

Time: 11:45 AM
Location: Hill 705
Abstract: In this talk,I present a continuous-time extension of the framework for modeling market microstructure, developed in our previous work. I use this extension to model the shape and dynamics of the Limit Order Book (LOB) between two consecutive trades. In this model, the LOB arises as an outcome of an equilibrium between multiple agents who have different beliefs about the future de- mand for the asset. These beliefs may change according to the information observed by the agents (e.g. represented by a relevant stochastic factor), implying a change in the shape of the LOB. This model allows one to see how changing the relevant information signal (which is given in a very general form in our model) affects the LOB. In particular, if the relevant signal is a function of the LOB itself, then, our approach allows one to model the “informational” impact of market events (as opposed to the “mechanical” impact that a market order makes, by eliminating certain limit orders instantaneously). On the mathematical side, we formulate the problem as a mixed control-stopping game, with a continuum of players. We manage to split the equilibrium problem into two parts, and represent one of them through a two-dimensional system of Reflected Backward Stochastic Differential Equations, and the other one with an infinite-dimensional fixed-point equation. Although both problems present mathematical challenges, we manage to prove existence of their solutions and show how they can be computed in a simple example.

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Department of Mathematics

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Rutgers University
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