Grasping Asymmetric Information in Market Impacts

Abstract

Abstract. We measure the price impacts across a correlated financial market by the responses to single and multiple trades. Focusing on the primary responses, we use an event time scale. We quantify the asymmetries of the distributions and of the market structures of cross-impacts, and find that the impacts across the market are asymmetric and non-random. Using spectral statistics and Shannon entropy, we visualize the asymmetric information in market impacts. Also, we introduce an entropy of impacts to estimate the randomness between stocks. We show that the useful information is encoded in the impacts corresponding to the small entropy. The stocks with large number of trades are more likely to impact others, while the less traded stocks have higher probability to be impacted by others.

How to build a cross-impact model from first principles: theoretical requirements and empirical results

“…Incoming orders are then modeled as independent Poisson processes. One key assumption is thus that the signed traded order flow of two assets is uncorrelated, contrary to intuition and empirical evidence (see for example in [3,17,20,21,22]). Nevertheless, studying a simplified version of the partial differential equation ruling the behaviour of the utility function of the market maker (the link between the solution of the original PDE and simplified PDE is not clear, see [10]), the authors of [8] find that the corrective term to the mark-to-market value of the assets in the utility of the market maker when he holds an inventory q is of the form −q Λq, where:…”

“…Wang et al [21,22] analyzed stocks and used empirical cross-responses between trade signs and prices to build propagator models for cross-impact, using only the direction of the trade (and therefore neglecting the influence of volumes). In [20], the authors define an entropy for impact between stocks: when this coefficient is high, there should be no cross-impact. To study the structure of cross-impact, they build a network which connects assets when the entropy coefficient is low.…”

How to Build a Cross-Impact Model from First Principles: Theoretical Requirements and Empirical Results

“…Incoming orders are then modeled as independent Poisson processes. One key assumption is thus that the signed traded order flow of two assets is uncorrelated, contrary to intuition and empirical evidence (see for example in [3,17,20,21,22]). Nevertheless, studying a simplified version of the partial differential equation ruling the behaviour of the utility function of the market maker (the link between the solution of the original PDE and simplified PDE is not clear, see [10]), the authors of [8] find that the corrective term to the mark-to-market value of the assets in the utility of the market maker when he holds an inventory q is of the form −q Λq, where:…”

“…Hence, we will drop the time subscript from both price changes and imbalances from now on. The interested reader is referred to [3,17,20] for more general approaches to this problem. In our stylized setting, the relation between prices and order flows can thus be written as:…”

“…Wang et al [21,22] analyzed stocks and used empirical cross-responses between trade signs and prices to build propagator models for cross-impact, using only the direction of the trade (and therefore neglecting the influence of volumes). In [20], the authors define an entropy for impact between stocks: when this coefficient is high, there should be no cross-impact. To study the structure of cross-impact, they build a network which connects assets when the entropy coefficient is low.…”