Optimal Execution with Rough Path Signatures

Abstract

We present a method for obtaining approximate solutions to the problem of optimal execution, based on a signature method. The framework is general, only requiring that the price process is a geometric rough path and the price impact function is a continuous function of the trading speed. Following an approximation of the optimisation problem, we are able to calculate an optimal solution for the trading speed in the space of linear functions on a truncation of the signature of the price process. We provide strong numerical evidence illustrating the accuracy and flexibility of the approach. Our numerical investigation both examines cases where exact solutions are known, demonstrating that the method accurately approximates these solutions, and models where exact solutions are not known. In the latter case, we obtain favourable comparisons with standard execution strategies.

Uncertain Execution in Order-Driven Markets

“…In financial applications, interesting research problems include a study of the effect that latency has on the financial performance of electronic trading strategies, e.g., market making, pairs trading and other statistical arbitrage strategies. In particular, extend the recent works of Kalsi et al (2020) and Cartea et al (2020) to account for latency. In these works, the authors use techniques from rough path theory to solve relevant algorithmic trading problems, where it is assumed that there is no delay between trade attempts and executions.…”

Neural-Signature Methods for Structured EHR Prediction

“…A key advantage of signature methods is a strong theoretical groundwork showing the signatures usefulness in non-parametric hypothesis testing [11] and algebraic geometry [36]. Machine learning applications have also been demonstrated in a growing variety of domains [10] including: healthcare [4,26,27,34], finance [3,23], action recognition [30,47] and hand-writing recognition [46].…”

Optimal stopping with signatures

“…This paper is motivated by another recent application of signatures, namely the solution of stochastic optimal control problems in finance. We follow the presentation of [KLPA20], where a signature-based approach for solving optimal execution problems is developed. In a nutshell, the strategy can be summarized as follows:…”