Significance of cross-excitation in bivariate Hawkes-based optimal execution

Determine whether adding cross-excitation terms to a bivariate Hawkes process for buy and sell market order arrivals in the German intraday electricity market yields a statistically significant additional reduction in cumulative execution costs compared with a univariate Hawkes process that models only self-excitation, when both are used to derive optimal liquidation strategies under the same transient price impact framework.

Background

The study calibrates Hawkes-process models to EPEX Spot limit order book data and derives an optimal execution strategy under a transient price impact framework. It evaluates both a univariate Hawkes model (self-excitation only) and a bivariate Hawkes model (including cross-excitation between buy and sell flows), comparing execution cost reductions against TWAP and VWAP benchmarks across hourly products.

While cumulative cost improvements are positive in the multivariate setting, the authors explicitly state uncertainty about whether these improvements are meaningfully larger than those obtained with the univariate model. Establishing statistical significance of any incremental benefit from cross-excitation would clarify whether the added model complexity is justified for practical optimal execution in intraday energy markets.