Do fundamentals shape the price response? A critical assessment of linear impact models

Vodret, Michele; Tóth, Bence; Mastromatteo, Iacopo; Benzaquen, Michael

doi:10.1080/14697688.2022.2114376

Cited by 1 publication

(2 citation statements)

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“…Theorem 2.10 is the first result that proves convergence of any estimator for a propagator, which is based on market price quotes. These results answer an open question that arises from [8,9,16,44,45] among others.…”

Section: Introductionsupporting

confidence: 58%

“…In order to quantify the price impact and hence the trading costs, the trader needs a good estimation of G and λ. Some estimators for discrete-time versions of the model were proposed in [8,16,44,45] and in Chapter 13.2 of [9], where only a finite amount of values {G(t n )} N n=1 are estimated for a predetermined grid 0 ≤ t 1 < ... < t n . However, even in this finite dimensional projection of the problem, the convergence of the estimators remains unproved, hence rigorous results on the estimation of G are considered as a long-standing open problem.…”

Section: Introductionmentioning

confidence: 99%

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Statistical Learning with Sublinear Regret of Propagator Models

Neuman¹,

Zhang²

2023

Preprint

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We consider a class of learning problems in which an agent liquidates a risky asset while creating both transient price impact driven by an unknown convolution propagator and linear temporary price impact with an unknown parameter. We characterize the trader's performance as maximization of a revenue-risk functional, where the trader also exploits available information on a price predicting signal. We present a trading algorithm that alternates between exploration and exploitation phases and achieves sublinear regrets with high probability. For the exploration phase we propose a novel approach for nonparametric estimation of the price impact kernel by observing only the visible price process and derive sharp bounds on the convergence rate, which are characterised by the singularity of the propagator. These kernel estimation methods extend existing methods from the area of Tikhonov regularisation for inverse problems and are of independent interest. The bound on the regret in the exploitation phase is obtained by deriving stability results for the optimizer and value function of the associated class of infinite-dimensional stochastic control problems. As a complementary result we propose a regression-based algorithm to estimate the conditional expectation of non-Markovian signals and derive its convergence rate.

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