Optimal Liquidation Strategy Based on Stochastic and Nonlinear Price Impact and Particle Swarm Optimization

Abstract:

The institutional investor selling a large block of shares in the market usually faces with liquidity risk declining the stock’s prices. In the paper, supposing that temporary impact is stochastic and nonlinear function of trading velocity, we establishes the discrete mathematical model and uses PSO to obtain the optimal liquidation strategies of risk aversion, which is a strict concave function. When analyzing the sensitivity of the parameters, we find that the curve becomes higher and steeper with the increase of the parameters or the decrease of , .As the parameter is tremendous, the curve is close to a horizon line.

• Periodical: Advanced Materials Research (Volumes 452-453)
• Pages: 607-612
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.452-453.607
• Online since: January 2012
• Authors: Fei Huang, Jia He Cao
• Keywords: Nonlinear, Optimal Liquidation Strategy, Particle Swarm Optimization (PSO), Stochastic

References

[1] Chan L K C, Lakonishok J. The behavior of stock price around institutional trades[J]. Journal of finance, 1995, 50: 1147—74.

DOI: 10.1111/j.1540-6261.1995.tb04053.x

[2] Bertsima D, Lo A.W. Optimal control of execution costs[J]. Journal of Financial Markets, 1998．1: l一50.

[3] Almgren R , Chriss N. Optimal execution of portfolio transactions[J]. Journal of Risk, 2000, 3(1), 5-39.

[4] Almgren R. Optimal execution with nonlinear impact functions and trading -enhanced risk [J]. Applied Mathematical Finance, 2003. 1.

DOI: 10.1080/135048602100056

[5] Dubil. Optimal Liquidation of Large Security Holding In Thin Market[J]. Journal of financial Economics . 2002(9).

[6] Zhong liming, Liu hailong, Wu chongfeng. Optimal control strategy of institutional investor's execution cost[J]. Journal of southeast university . 2004(2).

[7] Zhong li-ming, Liu hai-long, Wu chong-feng. Institution investors' optimal liquidation strategy[J]. Managemnt sciences in china. 2002 (5) : 18-22.

[8] Xueming Yang, Jinsha Yuan, Jiangye Yuan, Huina Mao. A modified particle swarm optimizer with dynamic adaptation[J]. Applied Mathematics and Computation 189 (2007) 1205–1213.

DOI: 10.1016/j.amc.2006.12.045

[9] Xueming Yang, Jinsha Yuan, Jiangye Yuan, Huina Mao. An improved WM method based on PSO for electric load forecasting[J]. Expert Systems with Applications 37 (2010) 8036–8041.

DOI: 10.1016/j.eswa.2010.05.085

[10] A. Schied , T. Schoneborn. Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets[J]. Finance Stoch(2009) 13: 181-204.

DOI: 10.1007/s00780-008-0082-8

[11] Christopher Ting, Mitch Warachka, Yonggan Zhao. Optimal liquidation strategies and their implications[J]. Economic dynamics&control . 31(2007)1431-1450.

DOI: 10.1016/j.jedc.2006.07.003

[12] Zvi Bodie. Investments[M]. China Machine Press. beijing. (2009).

[13] Chu xiao-jun, liu si-feng. The investigation of optimal liquidation under stochastic and nonlinear price impact[J]. Chinese Journal of management science. 2007(5).