How to Build a Cross-Impact Model from First Principles: Theoretical Requirements and Empirical Results
24 Pages Posted: 29 Apr 2020 Last revised: 4 Feb 2021
Date Written: April 3, 2020
Trading a financial instrument induces a price response on itself and on other correlated instruments, a phenomenon known as cross-impact. Unfortunately, empirical measures of cross-impact are affected by a large estimation error due to both the large number of interactions to infer and the strongly fluctuating nature of price returns. In this study we propose a principled approach that leverages simple consistency criteria (symmetries, no-arbitrage conditions, correlation and liquidity limit-case properties) in order to impose ex-ante properties that might be required for practical applications. We validate our approach on empirical data for several asset classes, thus determining which properties are desirable across multiple markets. In particular, our results show that two cross-impact models perform well in all markets studied but only one is suitable for other applications, such as optimal execution.
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