Optimal trade execution for Gaussian signals with power-law resilience

• Published in: Quantitative finance Vol. 22; no. 3; pp. 585 - 596
• Main Authors: Forde, Martin, Sánchez-Betancourt, Leandro, Smith, Benjamin
• Format: Journal Article
• Language: English
• Published: Bristol Routledge 04.03.2022; Taylor & Francis Ltd
• Subjects: Fredholm integral equations; Gaussian processes; High frequency trading; Integral equations; Market microstructure modeling; Optimal liquidation; Trading with signals; Transient price impact
• ISSN: 1469-7688; 1469-7696
• DOI: 10.1080/14697688.2021.1950919

We characterize the optimal signal-adaptive liquidation strategy for an agent subject to power-law resilience and zero temporary price impact with a Gaussian signal, which can include e.g an OU process or fractional Brownian motion. We show that the optimal selling speed is a Gaussian Volterra process of the form on , where and satisfy a family of (linear) Fredholm integral equations of the first kind which can be solved in terms of fractional derivatives. The term is the (deterministic) solution for the no-signal case given in Gatheral et al. [Transient linear price impact and Fredholm integral equations. Math. Finance, 2012, 22, 445-474], and we give an explicit formula for for the case of a Riemann-Liouville price process as a canonical example of a rough signal. With non-zero linear temporary price impact, the integral equation for becomes a Fredholm equation of the second kind. These results build on the earlier work of Gatheral et al. [Transient linear price impact and Fredholm integral equations. Math. Finance, 2012, 22, 445-474] for the no-signal case, and complement the recent work of Neuman and Voß[Optimal signal-adaptive trading with temporary and transient price impact. Preprint, 2020]. Finally we show how to re-express the trading speed in terms of the price history using a new inversion formula for Gaussian Volterra processes of the form , and we calibrate the model to high frequency limit order book data for various NASDAQ stocks.