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
Date Written: March 27, 2020
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
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