Applying regression techniques in designing optimal trade execution strategy for an asset

Abstract

The paper aims to construct an optimal trading strategy for procuring a large but fixed volume of a risky asset. The proposed approach splits a large block of trade into smaller packages to minimize the execution cost of the trade. In this study, we suggest an incipient price dynamics for the asset where we express its current market price as a convex combination of the price impervious to our anterior trade in the asset and the execution price carrying the impact of our anterior trade in it. We propose to apply the regression techniques to estimate the unaffected price of the asset. The formulated model is a convex quadratic optimization problem and thus computationally tractable. We evaluate the performance of the proposed model on five stocks namely, Apple, Microsoft, Coca-Cola, Amazon, and Netflix and conclude that the proposed model consistently achieves a lower execution cost than the one obtained from some other models existing in the literature.

Keywords:

• Optimal trade execution problem
• price dynamics of an asset
• quadratic programming problem
• quantile regression
• support vector quantile regression

2010 Mathematics Subject Classifications:

• 90C20
• 90C90

Acknowledgments

First author is thankful to the institute IIT Delhi, India, for research grant through GATE scholarship. The authors acknowledge the editor-in-chief and the learned referees for their critical comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 We observe that the expression in computing Var(${\tilde{P}}_{i-1}{\mathrm{e}}^{Z_i}$) on Page 589, lines 17–18, in [9] is wrong. The simplification of the expression missed on several nontrivial variance and covariance terms, which otherwise would have led to an unknown covariance matrix. Hence, the resultant problem would not have been the quadratic programming problem, as described on p. 589.

2 $K_{RBF}(x,x^{\mathrm{\prime }})=\exp (-\kappa \parallel x-x^{\mathrm{\prime }}{\parallel }^2)$, where $\kappa >0$ is a parameter. We took $\kappa =0.5$ in our experiments.

Additional information

Funding

First author is thankful to the institute Indian Institute of Technology Delhi – IIT Delhi, India, for research grant through GATE scholarship.