Convex Modeling of Price Cross-Impact over Time
Abstract
Transaction costs can make or break a trading strategy, particularly in relative-value trading of commodity and macro markets, where edges are a few basis points. Price impact is a central component of transaction cost. Price impact models usually include self-impact (a trade in a contract moves that contract's price) but omit two well-documented effects: cross-impact (a trade in one contract also moves the prices of related contracts) and transient impact (price impact decays over time, so an unwind recovers part of the entry cost). A model without these effects overprices the impact of relative-value trades, whose correlated legs are built and unwound over days, and so forgoes potentially profitable trades. This paper models both effects with a convex quadratic cost. In each period, a positive semidefinite matrix built from volatility, volume, and correlation forecasts couples trades across contracts. A power-law decay kernel then couples trades across periods. The resulting cost admits no price manipulation even when liquidity varies over the planning horizon. The model is demonstrated empirically on calendar spread trading of crude oil futures around the commodity index roll.
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BibTeX
@misc{yinjunwang2026convex,
title = {{Convex Modeling of Price Cross-Impact over Time}},
author = {Vincent Yinjun-Wang and Madeleine Udell},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04712},
eprint = {2609.04712},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04712},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Convex Modeling of Price Cross-Impact over Time
AU - Vincent Yinjun-Wang
AU - Madeleine Udell
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04712
UR - https://arxiv.org/abs/2609.04712
AB - Transaction costs can make or break a trading strategy, particularly in relative-value trading of commodity and macro markets, where edges are a few basis points. Price impact is a central component of transaction cost. Price impact models usually include self-impact (a trade in a contract moves that contract's price) but omit two well-documented effects: cross-impact (a trade in one contract also moves the prices of related contracts) and transient impact (price impact decays over time, so an unwind recovers part of the entry cost). A model without these effects overprices the impact of relative-value trades, whose correlated legs are built and unwound over days, and so forgoes potentially profitable trades. This paper models both effects with a convex quadratic cost. In each period, a positive semidefinite matrix built from volatility, volume, and correlation forecasts couples trades across contracts. A power-law decay kernel then couples trades across periods. The resulting cost admits no price manipulation even when liquidity varies over the planning horizon. The model is demonstrated empirically on calendar spread trading of crude oil futures around the commodity index roll.
ER -