Cross-impact and no-dynamic-arbitrage

Schneider, Michael; Lillo, Fabrizio

doi:10.1080/14697688.2018.1467033

Cited by 38 publications

(50 citation statements)

References 49 publications

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“…The second axiom that we consider involves dynamic arbitrages in the spirit of [1,9]. Even though these arbitrages cannot be exploited in our single-period setup, they would emerge by generalizing our setup to the multi-time step setting such as in [17], which is why we choose to also consider this class of arbitrages.…”

Section: Axiom 6 (Positive Semi-definiteness) the Cross-impact Model ...mentioning

confidence: 99%

“…However, this condition is not sufficiently restrictive to prescribe specific cross-impact models. Interestingly, the non-parametric study [17] calibrates a propagator model on bonds and finds statistically significant asymmetries at different estimation scales (weekly, bi-weekly and monthly) and conservative confidence levels.…”

Section: Introductionmentioning

confidence: 99%

“…In short, the prices of illiquid stocks is driven by the prices of liquid stocks. On the other hand, the paper [17] considered bond markets which, given their higher pairwise correlation, one may expect to show significant cross-impact. Using a similar approach, they fit a propagator model and find strong cross-impact as well as small, but statistically significant, asymmetries.…”

Section: Introductionmentioning

confidence: 99%

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

Tomas

Mastromatteo

Benzaquen

2022

Quantitative Finance

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Cross-impact, namely the fact that on average buy (sell) trades on a financial instrument induce positive (negative) price changes in other correlated assets, can be measured from abundant, although noisy, market data. In this paper we propose a principled approach 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. We review the empirical performance of a large number of cross-impact models, comparing their strengths and weaknesses on a number of asset classes (futures, stocks, calendar spreads). Besides showing which models perform better, we argue that in presence of comparable statistical performance, which is often the case in a noisy world, it is relevant to favor models that provide ex-ante theoretical guarantees on their behavior in limit cases. From this perspective, we advocate that the empirical validation of universal properties (symmetries, invariances) should be regarded as holding a much deeper epistemological value than any measure of statistical performance on specific model instances.

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Section: Axiom 6 (Positive Semi-definiteness) the Cross-impact Model ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Tomas

Mastromatteo

Benzaquen

2022

Quantitative Finance

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“…The first two properties are extremely important in the calibration of cross-impact models, as shown in [AKS16,SL18]: to perform pricing within a cross-impact setup, the matrix Λ should be SPD in order to ensure absence of price manipulation. This is not the case for a MLE, which is thus not suitable for practical purposes.…”

Section: Consistency Of Correlationsmentioning

confidence: 99%

The Multivariate Kyle Model: More is Different

Molino¹,

Mastromatteo²,

Benzaquen³

et al. 2020

SIAM J. Finan. Math.

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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 securities. We prove the unicity of a symmetric, positive definite solution for the impact matrix and provide insights on its interpretation. We explore its implications from the perspective of empirical market microstructure, and argue that it provides a sensible inference procedure to cure some pathologies encountered in recent attempts to calibrate cross-impact matrices. As an illustration, we determine the empirical cross impact matrix of US Treasuries, and compare the results with recent alternative calibration methods.

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“…Existence of an optimal liquidation strategy in their model is guaranteed if the decay kernel corresponds to a matrix-valued positive definite function but additional assumptions on the decay kernel are required for the optimal liquidation strategies to be well-behaved. In their recent paper, Schneider and Lillo [20] established necessary conditions on the size and impact of cross-impact for the absence of dynamic arbitrage in a continuous time version of [1] that can be directly verified on data.…”

Section: Introduction and Overviewmentioning

confidence: 98%

Multi-dimensional optimal trade execution under stochastic resilience

Horst

Xia

2019

Finance Stoch

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We provide a general framework for analyzing linear-quadratic multi-dimensional portfolio liquidation problems with instantaneous and persistent price impact and stochastic resilience. We show that the value function can be described by a multi-dimensional nonmonotone backward stochastic Riccati differential equations (BSRDE) with a singular terminal condition in one component. We prove the existence of a solution to the BSRDE system and characterise both the value function and the optimal strategy in terms of that solution. We prove that the solution to the liquidation problem can be approximated by the solutions to a sequence of unconstrained problems with increasing penalisation of open positions at the terminal time. Our proof is based on a much fine a priori estimate for the approximating BSRDE systems, from which we infer the convergence of the optimal trading strategies for the unconstrained models to an admissible liquidation strategy for the original problem.T 0 |f (t)| 2 dt) 1/2 , respectively ess sup t,ω |f (t, ω)|. * Financial support through the TRCRC 190 Rationality and competition; the economic performance of individuals and firms and d-fine GmbH is gratefully acknowledged. We thank Paulwin Graewe for valuable comments and suggestions.

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Cross-impact and no-dynamic-arbitrage

Cited by 38 publications

References 49 publications

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

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

The Multivariate Kyle Model: More is Different

Multi-dimensional optimal trade execution under stochastic resilience

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