Non-average price impact in order-driven markets

Abstract

We present a measurement of price impact in order-driven markets that does not require averages across executions or scenarios. Given the order book data associated with one single execution of a sell metaorder, we measure its contribution to price decrease during the trade. We do so by modelling the limit order book using state-dependent Hawkes processes, and by defining the price impact profile of the execution as a function of the compensator of a stochastic process in our model. We apply our measurement to a data set from NASDAQ, and we conclude that the clustering of sell child orders has a bigger impact on price than their sizes.

Continuous‐time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations

“…Finally, the online optimization algorithm can be used to train SDE models (including point process models) of limit order books (Bellani et al, 2021;Kumar, 2021;Lu and Abergel, 2018;Morariu-Patrichi & Pakkanen, 2022;Shi & Cartlidge, 2022). Order books involve large numbers of high-frequency events (∼ 10 5 − 10 6 events per day per stock) and high-dimensional dynamics (many price levels, each with limit order submissions and cancellations, as well as market orders, hidden orders, and transactions).…”

“…Due to the size of the datasets and the high-dimensionality, calibrating simulation models of order book dynamics to data are computationally challenging. Recent examples of such model frameworks for the simulation of the order books include Morariu-Patrichi and Pakkanen (2022), Bellani et al (2021), Shi and Cartlidge (2022), Lu and Abergel (2018), Kumar (2021). Morariu-Patrichi and Pakkanen (2022), Bellani et al (2021), Shi and Cartlidge (2022), Lu andAbergel (2018), andKumar (2021) develop stochastic point process models to model the event-by-event dynamics in order books.…”

“…Events arrive with stochastic intensity 𝜆 𝑡 , that is, lim Δ→0 ℙ[𝑁 * 𝑡+Δ −𝑁 * 𝑡 =1| 𝑡 ] Δ = 𝜆 * 𝑡 . For example, 𝑁 * 𝑡 could be the number of limit orders submitted to the order book by time 𝑡. Multidimensional point process models can model the dynamics of the entire order book (e.g., limit order submissions, cancellations, market orders, hidden orders, and transactions) Morariu-Patrichi and Pakkanen (2022), Bellani et al (2021).…”