Optimal Execution of Foreign Securities: A Double-Execution Problem with Signatures and Machine Learning

38 Pages Posted: 20 Apr 2020 Last revised: 10 May 2021

See all articles by Álvaro Cartea

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Imanol Perez Arribas

University of Oxford - Mathematical Institute

Leandro Sánchez-Betancourt

Imperial College London - Department of Mathematics

Date Written: March 27, 2020

Abstract

We employ the expected signature of equity and foreign exchange markets to derive an optimal double-execution trading strategy. The signature of a path of a stochastic process is a sequence of real numbers that provides a full description of the evolution of the process. The double-execution strategy maximises the wealth (in units of the domestic currency) of an investor who liquidates a block of shares in a foreign stock market. Our approach is model agnostic because we do not specify the dynamics of the market. We prove that the optimal strategy is a linear combination of the terms in the expected signature of the market and employ high-frequency data from Nasdaq and for various currencies to compute the signature of the market. Data for ten stocks and four currency pairs are employed to implement the strategy. Our results show that the performance of the signature-based double-execution strategy is superior than the performance of the benchmarks. In most cases, the outperformance increases further when the signature of the market is enhanced with the price dynamics of the SPY; a tracker of the Standard \& Poor's 500 index.

Keywords: Optimal execution, price impact, machine learning, high-frequency trading, signatures, cryptocurrency, illiquidity

Suggested Citation

Cartea, Álvaro and Perez Arribas, Imanol and Sánchez-Betancourt, Leandro, Optimal Execution of Foreign Securities: A Double-Execution Problem with Signatures and Machine Learning (March 27, 2020). Available at SSRN: https://ssrn.com/abstract=3562251 or http://dx.doi.org/10.2139/ssrn.3562251

Álvaro Cartea (Contact Author)

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Imanol Perez Arribas

University of Oxford - Mathematical Institute ( email )

Andrew Wiles Building
Radcliffe Observatory Quarter (550)
Oxford, OX2 6GG
United Kingdom

Leandro Sánchez-Betancourt

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
London, SW7 2AZ
United Kingdom

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
631
Abstract Views
2,103
rank
54,146
PlumX Metrics