算法交易、价差交易与风险控制算法交易.ppt

Click to edit Master title style,First Level,Second level,Third Level,Fourth Level,Fifth Level,*,算法交易,(2),市场冲击模型,1,业界标准模型,对股票市场冲击的直接估计,(Almgren,Robert F,Chee Thum,Emmanuel Hauptmann,及,Hong Li(2005),证券交易最佳执行方案,(Almgren,Robert F,及,Neil A,Chriss(2000),书目：,交易最优策略,(Kissell,Robert,及,Morton Glantz(2003),2,3,目录,第,1,节,引言,第,2,节,理论模型,第,3,节,数据,第,4,节,单一仓位的最优交易时间,第,5,节,示例,第,6,节,总结,第,7,节,公式详尽推导,参考文献,第,1,节,引言,引进了持久,/,临时冲击模型,采用截面非线性回归模型及高斯,-,牛顿最佳化演算法确定模型系数将虚拟变量引入各样交易策略,比较各种备选模型,获取并分析样本内外预测,对于以,min(EC+lamda*Risk),为目标的仓位，解决了最佳交易时间,T,提及未来开发和扩展,4,5,第,2,节,理论模型,基本问题及利害权衡,快速交易，你可以左右市场,等待交易，市场会变动,模拟交易中的问题,股价动态,：假定证券遵循算术布朗运动,交易成本即对市场的冲击,持久冲击,：交易将新信息传达给市场,;,市场调整证券价格,临时冲击：,由于即时性需求，价格出现短暂波动,6,交易前后净价变动,(I),：,交易后某个适当时间点,(,即最后一宗交易后半小时,),证券的价格和到达中价之间的差额。

与持久冲击相关交易指令遭受的实际平均冲击为,I,的一部分执行不足,(IS,或,J),：,买入指令中,不足指实际支付价与到达中价之差,卖出指令中,不足指到达中价与实收现金之差,临时冲击,为,J,和部分,I,的差额,即：指令中执行不足与平均持久冲击之差7,变量,X,：指令数量,t,0,t,1,t,n,分别指指令到达,(,时钟,),时间、首次交易时间、,最后交易时间0,1,n,分别指对应,t,0,t,1,t,n,的交易量时间交易量时间：时钟时间,t,为止，执行的平均日交易量百分比（小数）0=,1),减小,所以,E(IS),为,T,的递减函数,已知：,SD(IS),显然为,T,的递增函数,但以非线性的方式递增,所以,E(IS)+,SD(IS),将显示出,U,形曲线,最佳,T*,将与其底部对应,(,最小,),其一阶条件如下：,25,第五节：示例,请看香港股票,16,IS,策略,下一张,幻灯片,显示了在,X/ADV=20%,和,=0.001,条件下,E(IS)+,*SD(IS),的曲线图：,ADV,6,413,792,BTR,2,53,日成交量,0.26%,差幅,9,63 bps,年度性波动,14,。

14%,26,VWAP(X/ADV=20%,=0.005),：,T*=0.0818(,交易时间,),E(IS)=0.0513 bps,SD(IS)=2,3341 bps,27,IS(X/ADV=20%,=0.001),：,T*=0.109(,交易时间,),E(IS)=0.054 bps,SD(IS)=2,698 bps,28,ILWV(X/ADV=20%,=0.001),：,T*=0.4864(,交易时间,),E(IS)=0.0762 bps,SD(IS)=5,6934 bps,29,CLOSE(X/ADV=20%,=0.1),：,T*=0.0086(,交易时间,),E(IS)=0.2434 bps,SD(IS)=0.7568 bps,30,VWAP,策略：,Aggresiveness,T*(Volume Time),Risk(bps),Impact(bps),0.001,Most Passive,0.2464,4,0520,0.0468,0.005,Passive,0.0818,2,3341,0.0513,0.01,Nornal,0.0362,1,5529,0.0569,0.1,Aggressive,0.0013,0.2932,0.0940,1,Most Aggressive,0.0001,0.0664,0.1497,31,IS,策略：,Aggresiveness,T*(Volume Time),Risk(bps),Impact(bps),0.001,Most Passive,0.1092,2,。

6976,0.0543,0.005,Passive,0.0543,1,9014,0.0565,0.01,Nornal,0.0290,1,3896,0.0602,0.1,Aggressive,0.0013,0.2918,0.0942,1,Most Aggressive,0.0001,0.0664,0.1497,32,ILWV,策略：,Aggresiveness,T*(Volume Time),Impact(bps),Risk(bps),0.001,Most Passive,0.4864,0.0762,5,6934,0.005,Passive,0.1821,0.0821,3,4831,0.01,Nornal,0.0845,0.0900,2,3727,0.1,Aggressive,0.0032,0.1470,0.4588,1,Most Aggressive,0.0001,0.2498,0.0844,33,Close,策略,Aggresiveness,T*(Volume Time),Risk(bps),Impact(bps),0.001,Most Passive,1,0000,8,1630,0.1321,0.005,Passive,0.4401,5,。

4152,0.1398,0.01,Nornal,0.2164,3,7975,0.1515,0.1,Aggressive,0.0086,0.7568,0.2434,1,Most Aggressive,0.0002,0.1282,0.4243,34,通过各种策略、各种激进程度的冲击和风险的最优化组合，可以绘出,ETF,带35,第,6,节,总结,采用虚拟变量,针对不同策略的综合模型已被开发采用实例展示相关建模结果及模型的实用性,建模结果可完善现有算法及最终交易绩效,我们模型可以找到其主要用途之一的交易前系统现在可以正式开发了,36,第,7,节：公式详尽推导,求,K=J-I/2,随机变量的平均值和方差已知,其中,则,Y,的平均值为：,37,附录：公式详尽推导,求,K=J-I/2,随机变量的平均值和方差,(,接上页,),：,Y,的方差为：,38,附录：公式详尽推导,求,K=J-I/2,随机变量的平均值和方差,(,接上页,),：,已知,X,在以下平均值和方差呈正态分布,即得出,X,和,Y,的,协方差,39,附录,：公式详单,求,K=J-I/2,随机变量的平均值和方差,(,接上页,),：,所以,即得出,K,的平均值为零,方差为：,40,附录,：公式详单,高斯,-,牛顿最优化算法,基本理念是通过解决一系列线性最小二乘方问题,来得出非线性最小二乘方的答案。

假设,x(k),是,kth,的近似解,将,x(k),的非线性最小二乘方线性化,将原来的问题转化成线性最小二乘方的问题,使用常用的最小二乘法得出最小点,x(k+1),(k+1),的近似值接着我们比较两个近似值,看以下结论是否成立若成立,停止计算,答案已得出,;,否则,重复以上迭代,从数学上看,最小二乘方为：,fi(x),为,x,的非线性函数上述迭代如下：,41,附录,：公式详单,高斯,-,牛顿最优化算法,(,接上页,),其中：,且,42,附录,：公式详单,加权最小二乘法,此处根据误差大小加权的异方差,通常设原始回归方程式为：,若已知异方差形式,如：,该已知异方差可以得到提前纠正，转化得出以下方程式此新模照常由,最小二乘法估算,43,参考文献,Almgren,Robert F,Chee Thum,Emmanuel Hauptmann and Hong Li(2005),“Direct Estimation of Equity Market Impact”.,Almgren,Robert F(2001),“Optimal Execution with Nonlinear Impact Functions and Trading-Enhanced Risk”.,Almgren,Robert F and Neil A.Chriss(2000),“Optimal Execution of Portfolio Transactions”.,Chriss,Neil A.(1999),“Optimal Execution of Portfolio Transactions”.,Hora,Merrell(2005),“The Practice of Optimal Execution”,in Algorithmic Trading II,Institutional Investor,pp.52-63.,Institutional Investor(2005),Algorithmic Trading II,.,Kissell,Robert and Morton Glantz(2003),Optimal Trading Strategies,.,Kissell,Robert and Roberto Malamut(2005),“Algorithmic Decision-Making Framework”,in,Algorithmic Trading II,Institutional Investor,pp.82-91,Levy,H.and H.M.Markowitz.“Approximating Expected Utility By A Function Of Mean And Variance,American Economic Review,1979,v69(3),308-317.,44,参考文献,Manganelli,Simone(2002),“Duration,Volume and Volatility Impact of Trades”,Europe Central Bank Working Paper Series No.125.,Pindyck,Robert S.and Daniel L.Rubinfeld(1998),Econometric Models and Economic Forecasts(4,th,Edition),Irwin McGraw-Hill.,Rakhlin,Dmitry and George Sofianos(2005),“Choosing Benchmarks vs.Choosing Strategies,：,Part 2 Execution Strategies,：,VWAP or Shortfall”,in,Algorithmic Trading II,Institutional Investor,pp.75-81.,Sofianos,George(2005),“Choosing Benchmarks vs.Choosing Strategies,：,Part 1 Execution Benchmarks,：,VWAP or Pretrade Prices”,in,Algorithmic Trading II,Institutional Investor,pp.71-74.,Spierdijk,Laura,Theo E.Nijman,Arthur H.O.van Soest(2004),“Temporary and Permanent Price Effects of Tr。