Seminar Event Detail


Financial/Actuarial Mathematics

Date:  Thursday, May 26, 2016
Location:  1360 East Hall (4:00 PM to 5:00 PM)

Title:  Endogenous Formation of Limit Order Books And Dynamics Between Trades

Abstract:   In this talk, I will present a modeling framework in which the shape and dynamics of a Limit Order Book (LOB) arise endogenously from an equilibrium between multiple market participants (agents). This approach allows us to formulate tractable continuum-of-players games closely capturing the micro-level mechanics of LOB-based exchanges.

In the first part of my talk, I will talk about a discrete time version of our model, in which we analyze the effects of trading frequency on market liquidity in a very general setting. In particular, we show that the higher trading frequency increases market efficiency if the agents choose to provide liquidity in equilibrium. However, the higher trading frequency also makes markets more fragile, in the following sense: in a high-frequency trading regime, the agents choose to provide liquidity in equilibrium if and only if they are market-neutral (i.e. their beliefs satisfy certain martingale property).

In the second part of my talk, I will formulate a continuous time version of our model to analyze the behavior of the shape and dynamics of LOB between two consecutive trades. In this model, the LOB arises as an outcome of an equilibrium between the agents, who have different beliefs about the future demand for the asset. On the mathematical side, we formulate the problem as a mixed control-stopping game, which under certain assumptions splits into two parts: a two-dimensional system of Reflected Backward Stochastic Differential Equations and an additional fixed-point problem. We prove the existence of solutions to those problems and show how they can be computed in a simple example.

(joint with Sergey Nadtochiy)

Files: 3948_talk.pdf


Speaker:  Roman Gayduk
Institution:  UM

Event Organizer:   Erhan Bayraktar    erhan@umich.edu

 

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