A characterisation of cross-impact kernels

@article{Rosenbaum2021ACO,
  title={A characterisation of cross-impact kernels},
  author={Mathieu Rosenbaum and Mehdi Tomas},
  journal={Capital Markets: Market Microstructure eJournal},
  year={2021}
}
  • M. RosenbaumM. Tomas
  • Published 19 July 2021
  • Mathematics
  • Capital Markets: Market Microstructure eJournal
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 parametrisations 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… 
View on SSRN
arxiv.org
2 Citations
Background Citations
2

2 Citations

Cross Impact in Derivative Markets

We introduce a linear cross-impact framework in a setting in which the price of some given financial instruments (derivatives) is a deterministic function of one or more, possibly tradeable,…

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

A principled approach is proposed that allows to perform model selection for cross-impact models, showing that symmetries and consistency requirements are particularly effective in reducing the universe of possible models to a much smaller set of viable candidates, thus mitigating the effect of noise on the properties of the inferred model.

References

SHOWING 1-10 OF 37 REFERENCES

Cross Impact in Derivative Markets

We introduce a linear cross-impact framework in a setting in which the price of some given financial instruments (derivatives) is a deterministic function of one or more, possibly tradeable,…

Cross-impact and no-dynamic-arbitrage

We extend the ‘No-dynamic-arbitrage and market impact’-framework of Gatheral [Quant. Finance, 2010, 10(7), 749–759] to the multi-dimensional case where trading in one asset has a cross-impact on the…

Dissecting cross-impact on stock markets: an empirical analysis

The vast majority of market impact studies assess each product individually, and the interactions between the different order flows are disregarded. This strong approximation may lead to an…

Multivariate Transient Price Impact and Matrix-Valued Positive Definite Functions

A model for linear transient price impact for multiple assets that takes cross-asset impact into account and single out properties that need to be imposed on the decay kernel so that the model admits well-behaved optimal trade execution strategies.

No-dynamic-arbitrage and market impact

Starting from a no-dynamic-arbitrage principle that imposes that trading costs should be non-negative on average and a simple model for the evolution of market prices, we demonstrate a relationship…

Cross-response in correlated financial markets: individual stocks

Abstract Previous studies of the stock price response to trades focused on the dynamics of single stocks, i.e. they addressed the self-response. We empirically investigate the price response of one…

No‐arbitrage implies power‐law market impact and rough volatility

Market impact is the link between the volume of a (large) order and the price move during and after the execution of this order. We show that in a quite general framework, under no‐arbitrage…

Strategic Cross-Trading in the U.S. Stock Market

We model and test for the role of heterogeneously informed, strategic multi-asset speculation for cross-price impact—the impact of trades in one asset on the prices of other (even unrelated)…

The Multivariate Kyle Model: More is Different

We reconsider the multivariate Kyle model in a risk-neutral setting with a single, perfectly informed rational insider and a rational competitive market maker, setting the price of n correlated…

From microscopic price dynamics to multidimensional rough volatility models

This work uses Hawkes processes to build microscopic models that accurately reproduce high-frequency cross-asset interactions and investigate their long-term scaling limits, and recovers classical properties of high-dimensional stock correlation matrices.