Abstracts

Nowadays, High-Frequency-Trading is a highly automated business and automatic trading is introduced in the major stock exchanges. One participant in these markets wants to trade a large quantity of shares within a given time via limit order or market order. The main question is how to slice the order, when and how to trade optimally. In this research, we exclusively consider optimal order execution in an illiquid market where this participant is the only price taker. We address optimal execution problem for market order trading under different micro structure such as order book shape, resilience of price impact. In such market, the trader will take offers in the limit order book and seeking for the optimal trade-off between liquidity and minimal price impact.
In this research, discrete market order flow can be viewed as occurring at random times, say according to a Poisson process. The minimizing of total price impact can be done via splitting large orders into smaller pieces in a given time frame. The highlight of the study is to construct numeric boundaries based on a discrete order flow. Whenever we observe the bidding price hit or higher than the boundary, we will execute the amount of notional that is associating with this specific boundary.
We start from toy example where the analytical boundary for single unit execution is derived. Later on we extend the model to multi unit order case and construct different boundary numerically via Monte Carlo simulation method. With numerical experiments, we study the converge of algorithm to optimal execution strategy regarding to time-dependent parameters such as order book shapes, order intensity and resilience function and other constraints on optimal strategy.