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Admissible Cross-Impact Kernels for Martingale Prices and Manipulation-Free Trading

Article arXiv papers · Author: Mathieu Rosenbaum et al.
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Summary

This work analyzes cross-impact: how trading one asset can move its own price and the prices of other assets. It studies kernel-based models and parameter choices suitable for trading applications, focusing on two properties. Martingale-admissible kernels make prices martingales while accounting for anticipated future order flow; no-statistical-arbitrage-admissible kernels rule out possible price manipulation.

The authors characterize the relationship and overlap between these two classes and give formulas for calibrating cross-impact kernels from data. They illustrate the results with S&P 500 futures data. This provides a framework for model selection and empirical calibration, though the short description does not report specific calibration outcomes or explain how the framework performs under different market conditions. Its contribution is principally in characterizing model constraints and procedures, not in presenting a trading strategy or measured returns.

Key ideas

  • Cross-impact models describe how trades in one asset affect prices across assets.
  • Martingale-admissible kernels account for expected order flow while preserving martingale prices.
  • No-statistical-arbitrage-admissible kernels exclude price manipulation opportunities.
  • The study characterizes the overlap between the two admissible kernel classes.
  • It supplies calibration formulas and illustrates them with S&P 500 futures data.

Tags

FuturesMarket microstructureExecutionStatistics
Full text
# A characterisation of cross-impact kernels


# A characterisation of cross-impact kernels









Trading a financial asset pushes its price as well as the prices of other assets, a phenomenon known as cross-impact. We consider a general class of kernel-based cross-impact models and investigate suitable parameterisations for trading purposes. We focus on kernels that guarantee that prices are martingales and anticipate future order flow (martingale-admissible kernels) and those that ensure there is no possible price manipulation (no-statistical-arbitrage-admissible kernels). We determine the overlap between these two classes and provide formulas for calibration of cross-impact kernels on data. We illustrate our results using SP500 futures data.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.