Optimal trade execution for Gaussian signals with power-law resilience
研究了在幂律弹性和零暂时价格冲击下，面对高斯信号（如OU过程或分数布朗运动）时，交易者的最优信号自适应清算策略，并给出了策略的显式解和校准方法。
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 u∗t\n is a Gaussian Volterra process of the form u∗(t)=u0(t)+u¯(t)+∫t0k(u,t)dWu\n on [0,T)\n, where k(⋅,⋅)\n and u¯\n satisfy a family of (linear) Fredholm integral equations of the first kind which can be solved in terms of fractional derivatives. The term u0(t)\n 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 k(u,t)\n 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 k(u,t)\n 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 ∫t0g(t−s)dWs\n, and we calibrate the model to high frequency limit order book data for various NASDAQ stocks.