Optimal portfolio execution with a Markov chain approximation approach

We study the problem of executing a large multi-asset portfolio in a short time period where the objective is to find an optimal trading strategy that minimizes both the trading cost and the trading risk measured by quadratic variation. We contribute to the existing literature by considering a multi-dimensional geometric Brownian motion model for asset prices and proposing an efficient Markov chain approximation (MCA) approach to obtain the optimal trading trajectory. The MCA approach allows us not only to numerically compute the optimal strategy but also to theoretically analyse the influence of factors such as price impact, risk aversion and initial asset price on the optimal strategy, providing both quantitative and qualitative guidance on the trading behaviour. Numerical results verify the theoretical conclusions in the paper. They further illustrate the effects of cross impact and correlations on the optimal execution strategy in a multi-asset liquidation problem.

[1]  Sebastian Jaimungal,et al.  Trading co‐integrated assets with price impact , 2015, Mathematical Finance.

[2]  Hong Liu,et al.  Optimal Consumption and Investment with Transaction Costs and Multiple Risky Assets , 2004 .

[3]  Jingnan Chen,et al.  Theory of Leveraged Portfolio Selection Under Liquidity Risk , 2020 .

[4]  Robert Almgren,et al.  Optimal execution of portfolio trans-actions , 2000 .

[5]  Claus Munk.  The Markov chain approximation approach for numerical solution of stochastic control problems: experiences from Merton's problem , 2003, Appl. Math. Comput..

[6]  Duane J. Seppi,et al.  Episodic Liquidity Crises: Cooperative and Predatory Trading , 2007 .

[7]  Michael Monoyios.  Option pricing with transaction costs using a Markov chain approximation , 2004 .

[8]  Garleanu Nicolae,et al.  Dynamic Trading with Predictable Returns and Transaction Costs , 2009 .

[9]  Ananth N. Madhavan.  Market Microstructure: A Survey , 2000 .

[10]  P. Boyle,et al.  Numerical Evaluation of Multivariate Contingent Claims , 1989 .

[11]  Paolo Pasquariello,et al.  Strategic Cross-Trading in the U.S. Stock Market , 2009 .

[12]  H. Tookes.  Information, Trading and Product Market Interactions: Cross-Sectional Implications of Informed Trading , 2008 .

[13]  Jim Gatheral,et al.  Optimal Trade Execution under Geometric Brownian Motion in the Almgren and Chriss Framework , 2011 .

[14]  Jiang Wang,et al.  Dynamic Portfolio Execution , 2017, Manag. Sci..

[15]  P. Date,et al.  Two methods for optimal investment with trading strategies of finite variation , 2012 .

[16]  S. Ross,et al.  Option pricing: A simplified approach☆ , 1979 .

[17]  J. Sherman,et al.  Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix , 1950 .

[18]  D. Marazzina,et al.  Passive portfolio management over a finite horizon with a target liquidation value under transaction costs and solvency constraints , 2016 .

[19]  Charles Chang,et al.  Trading imbalances, predictable reversals, and cross-stock price pressure , 2008 .

[20]  Robert J. Elliott,et al.  Optimal Portfolio Execution Problem With Stochastic Price Impact , 2019, Autom..

[21]  J. Harford,et al.  Correlated Order Flow: Pervasiveness, Sources, and Pricing Effects , 2005 .

[22]  Jiming Peng,et al.  Analytical Results and Efficient Algorithm for Optimal Portfolio Deleveraging with Market Impact , 2013, Oper. Res..

[23]  Peter A. Forsyth,et al.  Optimal trade execution: A mean quadratic variation approach , 2012 .

[24]  Jonathan Levav,et al.  Process Utility and the Effect of Inaction Frames , 2018, Manag. Sci..

[25]  Duane J. Seppi,et al.  Common Factors in Prices, Order Flows and Liquidity , 1998 .

[26]  D. Bertsimas,et al.  Optimal control of execution costs , 1998 .