Essays on market liquidity

Abstract

In the first chapter of my Thesis I propose a model of front-running in noisy market environment. I demonstrate that even if the front-runner/predator has no initial knowledge about the position of a distressed trader he will be still able to front-run his orders in a linear Bayesian-Nash equilibrium. This is possible because initial orders of the distressed trader tend to reveal his initial position. The contribution of this chapter is also in the analysis of long-term dynamics of predatory trading under Gaussian uncertainty. Second chapter treats about the dark-pools of liquidity which are highly popular systems that allow participants to enter unpriced orders to buy or sell securities. These orders are crossed at a specified time at a price derived from another market. I present an equilibrium model of coexistence of dark-pools of liquidity and the dealer market. Dealer market provides the immediate execution, whereas the dark-pool of liquidity provides lower cost of trading. Risk-averse agents in equilibrium optimally choose between safe dealer market and cheaper dark-pool of liquidity. In the third chapter I solve for a partial-equilibrium optimal consumption and investment problem, when one of the investment assets is traded infrequently. Opportunity to trade the "illiquid asset" arises upon the occurrence of a Poisson event. Only when such event occurs a trader is able to change (increase or decrease) her position in the illiquid asset. The investor can consume continuously from the bank account. After deriving HJB equation, I analyze in details the implications of illiquidity on the optimal level of consumption, allocation and welfare. The optimal policy is solved using algorithm from aeronautics