Optimal Execution Strategy Of High Frequency Trading

As the liquidity provider for security market,market makers play an important role in security trading.In general,they have a great demand for the security trading and rely on algorithmic trading.Large orders always bring the adverse shock to security price,as a result,increase transaction costs.Thus,it’s of great significance to study how to split large orders into small orders under high frequency trading,that’s what we call the optimal execution strategy.Based on discrete static high frequency trading model and the framework of limit order book,with the underlying asset price following a geometric Brownian motion,we consider the intertemporal dynamics of the supply/demand,measure the resilience of liquidity,and establish the objective function of execution cost for a given order.Also we suppose that market maker can estimate the liquidity change after high frequency trading according to the news inferred from the order flow,and then introduce the market reaction and risk preference to the model.We derive the analytical properties of our model in finding the optimal execution strategy with dynamic programming algorithm.We show that the execution cost can be reduced after increasing trading frequency with a simulation study.In addition,we conduct a numerical simulation and show that the execution cost will be increased as the cost of risk balance.