无漂移算术布朗运动下股指期货套期保值连续出清策略

中国管理科学 ›› 2014, Vol. 22 ›› Issue (2): 10-15.

无漂移算术布朗运动下股指期货套期保值连续出清策略

唐衍伟, 陈刚, 刘喜华

青岛大学经济学院, 山东青岛 266071

收稿日期:2012-07-29 修回日期:2012-12-18 出版日期:2014-02-20 发布日期:2014-02-18
基金资助:
国家自然科学基金资助项目（70971071）

Continuous Optimal Liquidation of the Single Hedged Stock under Arithmetic Brownian Movements without Drift

TANG Yan-wei, CHEN Gang, LIU Xi-hua

School of Economics, Qingdao University, Qingdao 266071, China

Received:2012-07-29 Revised:2012-12-18 Online:2014-02-20 Published:2014-02-18

摘要/Abstract

摘要： 假定股票和期货服从无漂移项的算术布朗运动，投资者效用为均值-方差形式，价格冲击为线性，在连续时间框架下，求解单只股票与股指期货套期保值同步出清问题，得到出清轨迹。参数分析表明：当风险厌恶程度较大时、组合标准差越大，投资者倾向于在出清初期出清较大规模的头寸，以降低后期的风险；当ρ<0，随套期保值比的增加，投资者更倾向于快速的出清过程，当ρ>0则相反；在给定套期保值比的情况下，出清速率与相关系数呈反向变化。

关键词: 股指期货, 套期保值, 出清策略

Abstract: A hedging strategy without considering transaction cost is uncompleted which would bring risk to the portfolio. Considering the investor has mean-variance utility, the stock and index futures is the arithmetic Brownian movements without drift and market impact is linear, the continuous liquidation trajectory of the single hedged stock is derived under given time span. The parameters analysis shows that the investors are likely to trade quickly if they are more risk aversion or the portfolio's variance is larger; if the correlation coefficient is negative, they want to execute more quickly and vice versa; the liquidation velocity changes opposite to the correlation coefficient under the given hedging ratio.

Key words: stock index futures, hedging, liquidation

中图分类号:

F830.9

唐衍伟, 陈刚, 刘喜华. 无漂移算术布朗运动下股指期货套期保值连续出清策略[J]. 中国管理科学, 2014, 22(2): 10-15.

TANG Yan-wei, CHEN Gang, LIU Xi-hua. Continuous Optimal Liquidation of the Single Hedged Stock under Arithmetic Brownian Movements without Drift[J]. Chinese Journal of Management Science, 2014, 22(2): 10-15.

参考文献

[1] Lawrence C, Robinson G. Liquidity, dynamic hedging and value at risk[J]. Risk Management for Financial Institutions, 1997, 1(9):63-72.
[2] Jarrow R, Subramanisan A. Mopping up liquidity[J]. Risk, 1997, 10: 170-173.
[3] Bertsimas D, Lo A W. Optimal control of execution costs[J]. Journal of Financial Markets, 1998, 1(1): 1-50.
[4] Almgren R, Chriss N. Value under liquidation[J]. Risk, 1999, 12(12): 61-63.
[5] Almgren R, Chriss N, Optimal execution of portfolio transactions[J], Journal of Risk, 2000, 3: 5-39.
[6] Huberman G, Stanzl W. Optimal liquidity trading[R]. Working paper, Columbia University, 2001.
[7] Berkowitz J. Incorporating liquidity risk into VaR models[R]. Working Paper, 2000.
[8] Almgren R. Optimal execution with nonlinear impact functions and trading-enhanced risk[R]. Working paper, 2001.
[9] Dubil R. The modeling of liquidity in the valu E-at-risk framework[D]. Connecticut: University of Connecticut 2001.
[10] Dubil R. Optimal liquidation of large security holding in thin market[M]. Journal of Financial Economics, 2002.
[11] M B. Strategic trading in illiquid markets[M]. Berlin Heidelberg: Springer-Verlag, 2005.
[12] Subramanian A. Optimal liquidation by a large investors[J]. SIAM Journal on Applied Mathematics, 2007.
[13] Kim S J, Boyd S. Optimal execution under time-inhomogeneous price impact and volatility[J].Preprint, 2008.
[14] 林辉.金融市场微观结构视角的La-VaR模型[D].南京:东南大学, 2004.
[15] 胡小平. La-ES与最优变现策略模型研究[D].上海:上海交通大学, 2006.
[16] 储小俊.在随机非线性价格冲击下的最优变现策略研究[J].中国管理科学, 2007, 15(5): 137-142.
[17] 刘宣会. 于随机Lagrange方法的最优套期保值策略[J].系统工程理论实践, 2010, 30(6): 1034-1039.
[18] 唐衍伟.算术布朗运动下股指期货套期保值离散出清策略[J].系统工程理论实践, 2012.