Cross-impact and no-dynamic-arbitrage

TL;DR

This paper extends a market impact framework to multiple assets, deriving theoretical limits for cross-impact and testing these on sovereign bond data, revealing violations of symmetry conditions that are not arbitrageable due to bid-ask spreads.

Contribution

It generalizes the no-dynamic-arbitrage framework to multi-asset settings and empirically tests the derived theoretical constraints on real market data.

Findings

Cross-impact must be linear and odd in trading intensity.

Cross-impact symmetry is often violated in real data.

Violations are not arbitrageable due to bid-ask spreads.

Abstract

We extend the "No-dynamic-arbitrage and market impact"-framework of Jim Gatheral [Quantitative Finance, 10(7): 749-759 (2010)] to the multi-dimensional case where trading in one asset has a cross-impact on the price of other assets. From the condition of absence of dynamical arbitrage we derive theoretical limits for the size and form of cross-impact that can be directly verified on data. For bounded decay kernels we find that cross-impact must be an odd and linear function of trading intensity and cross-impact from asset $i$ to asset $j$ must be equal to the one from $j$ to $i$. To test these constraints we estimate cross-impact among sovereign bonds traded on the electronic platform MOT. While we find significant violations of the above symmetry condition of cross-impact, we show that these are not arbitrageable with simple strategies because of the presence of the bid-ask spread.