Liquidity Effects of Trading Frequency

In this article, 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). We use the proposed modeling framework to analyze the effects of trading frequency on 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, it 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 an endogenous liquidity crisis (aka flash crash) in the market. This framework enables us to provide more insight into how such a liquidity crisis unfolds, connecting it to the so-called adverse selection effect.Comment: Accepted in Mathematical Financ

Discrete Bidding Strategies for a Random Incoming Order

This paper is concerned with a model of a one-sided limit order book, viewed as a noncooperative game for n players. Agents offer various quantities of an asset at different prices, ranging over a finite set Ων = {(i/ν)P; i = 1,...,ν}, competing to fulfill an incoming order, whose size X is not known a priori. Playerscan have different payoff functions, reflecting different beliefs about the fundamental value of the asset and probability distribution of the random variable X. For a wide class of random variables, we prove that the optimal pricing strategies for each seller form a compact and convex set. By a fixed point argument, this yields the existence of a Nash equilibrium for the bidding game. As ν → ∞, we show that the discrete Nash equilibria converge to an equilibrium solution for a bidding game where prices range continuously over the whole interval [0,P]

Game-Theoretic Approach for Modeling Market Microstructure

This thesis is devoted to investigating possible approaches to endogenous modeling of market microstructure of an auction-based exchange. In chapter II we develop the framework in discrete time and apply it to understanding the economics of trading at high frequency. In chapter III we adapt our modeling approach to continuous time and develop a rich beliefs-driven model of limit-order book evolution between two trades. In the last chapter we introduce discrete admissible prices (i.e. a finite tick size) into our model and investigate the special spatial structures of the equilibria this produces. Given the novelty of the approach, we have to solve somewhat unusual mathematical problems throughout. We derive a novel estimate of conditional tails of general Ito processes in chapter II, solve a 'non-monotone oblique reflection' RBSDE system and a discontinuous infinite-dimensional fixed point problem in chapter III, and solve a system of control-stopping problems discontinuously coupled through stopping barriers in chapter IV. We also develop some numerical examples in chapters II and III to illustrate the features of our models and indicate possible applications.PHDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138688/1/gayduk_1.pd