In this work, we 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). On the one hand, the new framework captures very closely the true, micro-level, mechanics of an auction-style exchange. On the other hand , it uses the standard abstractions of games with continuum of players (in particular, the mean field game theory) to obtain a tractable macro-level description of the LOB. We use the proposed modeling framework to analyze the effects of trading frequency on the liquidity of the market 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, we also show that the higher trading frequency  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). The theoretical results are illustrated with numerical examples .
In this work, we present a discrete time modeling framework, in which the shape and dynamics of a Limit Order Book (LOB) arise endogenously from an equilibrium between multiple market participants (agents). The new framework captures very closely the true, micro-level, mechanics of an auction-style exchange. At the same time , it uses the standard abstractions of a continuum-player game to obtain a tractable macro-level description of the LOB. We use the proposed modeling framework to analyze the effects of trading frequency on the market liquidity in a very general setting. In particular, we demonstrate the dual effect of high trading frequency. On the one hand, the higher frequency increases market efficiency , if the agents choose to provide liquidity in equilibrium. On the other hand, the higher trading frequency also makes markets more fragile, in the sense that the agents choose to provide liquidity in equilibrium only if they are market-neutral (i.e. their beliefs satisfy certain martingale property). Even a very small deviation from market-neutrality may cause the agents to stop providing liquidity, if the trading frequency is sufficiently high, which represents a self-inflicted liquidity crises (aka flash crash) in the market. This framework allows us to provide more insight into how such a liquidity crises unfolds, connecting it to the so-called adverse selection effect .
R
modeling framework
discrete time modeling framework,
R
On the one hand, the
The
R
On the other hand
At the same time
R
games with continuum of players (in particular, the mean field game theory)
a continuum-player game
R
liquidity of the market
market liquidity
R
show that the higher trading frequency
demonstrate the dual effect of high trading frequency. On the one hand, the higher frequency
A
,
R
However, we also show that
On the other hand,
A
also
R
following sense : in a high-frequency trading regime,
sense that
D
if and
R
The theoretical results are illustrated with numerical examples
Even a very small deviation from market-neutrality may cause the agents to stop providing liquidity, if the trading frequency is sufficiently high, which represents a self-inflicted liquidity crises (aka flash crash) in the market. This framework allows us to provide more insight into how such a liquidity crises unfolds, connecting it to the so-called adverse selection effect