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

38 Pages Posted: 20 Apr 2020

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

University of Oxford

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 the domestic currency of an investor who liquidates a block of shares in a foreign stock market and the proceeds from the sale are exchanged into the investor's domestic currency. 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. Our results show that the signature-based double-execution strategy considerably outperforms various benchmarks that use single-execution strategies (one for the shares and one for the currency). The outperformance is more pronounced for the illiquid stocks and the illiquid domestic currencies we study.

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

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

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