The Research On High-frequency Trading And Optimal Execution Based On Bayesian Update

As a new algorithmic trading strategy,high-frequency trading has been developed rapidly recently.However,it could not be promoted in large-scale in China due to some restrictions such as hard ware and policy.In European and American,high-frequency trading also experienced active and inactive period.Even though,the markets outside China are more likely to adapt the high-frequency trading strategy.There are pros and cons in high-frequency trading:the pros are that speedy trading brings about the high liquidity,which is good for the market.Also high-frequency trading gives traders much more steady income.Yet the cons should not be ignored:high-frequency trading is hard to be supervised and its convenience may be unfair to normal traders.Optimal execution emerges in 1850s discovered by Markowitz who devotes himself to Mean-Variance method.Later Almgren and Chriss(2000)apply Mean-Variance model to optimal execution.In this paper,the author combines high-frequency trading and optimal execution and present us a new view.First,the author shows some background of high-frequency trading.In addition,some papers that are cited are discussed in the second chapter.After that Bayesian study and optimal execution strategy are given in the third chapter.In the fourth chapter,the author first models a trader not trading,just holding a bunch of cashes and stocks till the terminal time.The result gives us expected utility function.The author analyzes the result and calculates the best time to begin his trading.Bayesian update is used to revise math model.Reservation price,also called indifferent price,is defined,which is very useful to solve PDE.Consequently,HJB equations are used to solve stochastic optimal control problem and the best bid and ask quotes are given.The author results seem to be perfect,but it still has a lot of drawbacks.First,the number of stock in trader's hand could be varied continually instead of discretely.Second,utility function should be better chosen exponent utility function.Third,bid and ask orders arrival rate are different,not in the same form.