Convex Modeling of Price Cross-Impact over Time

RESUMO

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 but omit cross-impact and transient effects. A model without these effects overprices trades, whose correlated legs are built and unwound over days, 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 a commodity index roll.