Convex Modeling of Price Cross-Impact over Time

Battle Count: 74

Highly relevant to quantitative trading. The paper directly addresses transaction cost modeling for multi-period portfolio construction, which is central to relative-value trading strategies. The convexity guarantee and no-price-manipulation property are practically important for compliance. The empirical demonstration on WTI calendar spreads around index rolls is a concrete, actionable trading application. The model's ability to capture cross-impact netting and transient impact recovery directly affects trade sizing and timing decisions.

The mathematical model is elegant but requires careful implementation: constructing PSD matrices from volatility/volume/correlation forecasts, building the block matrix A with Kronecker product structure, solving a convex optimization with CVaR constraints, and estimating EWMA volatilities and correlations. The convexity proof is non-trivial (mixture of exponentials + Cauchy characteristic function). Practical implementation requires liquidity forecasting, correlation estimation, and handling of time-varying parameters. The optimization itself is standard convex programming but the full pipeline is moderately complex.

The paper uses public data (EIA daily settlements, CFTC volume reports, S&P GSCI methodology) and provides detailed parameter specifications. However, dollar volumes are simulated rather than using licensed exchange data, impact scaling parameters ℓ_i are set to 1 following prior work rather than learned, and the return forecast methodology is simplified. The mathematical model is fully specified and reproducible, but empirical results depend on simulated liquidity data.