Cross-Impact and No-Dynamic-Arbitrage

33 Pages Posted: 23 Dec 2016 Last revised: 26 Aug 2017

See all articles by Michael Schneider

Michael Schneider

Deutsche Bundesbank; Goethe University Frankfurt

Fabrizio Lillo

Università di Bologna

Date Written: August 25, 2017


We extend the “No-dynamic-arbitrage and market impact”-framework of Jim Gatheral [Quantitative Finance, 10(7): 749-759 (2010)] to the multidimensional 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.

Keywords: Market Impact, Dynamic Arbitrage, Cross-Impact, MOT, Sovereign Bonds

Suggested Citation

Schneider, Michael and Lillo, Fabrizio, Cross-Impact and No-Dynamic-Arbitrage (August 25, 2017). Available at SSRN: or

Michael Schneider (Contact Author)

Deutsche Bundesbank ( email )

Wilhelm-Epstein-Str. 14
Frankfurt/Main, 60431

Goethe University Frankfurt

Grüneburgplatz 1
Frankfurt am Main, 60323

Fabrizio Lillo

Università di Bologna ( email )

Via Zamboni, 33
Bologna, 40126

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