Cross-product Modelling in Continuous Intraday Electricity Markets via Hawkes Processes

As renewable energy integration accelerates, intraday continuous (IDC) electricity markets have become essential for short-term balancing. However, the simultaneous trading of overlapping contracts with varying granularities creates complex, hidden liquidity dependencies that are critical to market stability but remain poorly understood. This paper proposes a multivariate State-Dependent Hawkes Process (SDHP) to model cross-product liquidity dynamics between Quarter-Hourly and Hourly IDC contracts. To determine how cross-product effects vary under different market conditions, we classify the trading sessions into two distinct regimes: 'Normal' and 'Stressed', based on a composite metric of the bid-ask spread, mid-price volatility and queue imbalance. The model is calibrated on the first month of each quarter of 2024 using level 3 limit order book (LOB) data from the Dutch EPEX SPOT IDC market. We find that order flow is overwhelmingly self-driven, with roughly 95\% of orders arriving in reaction to earlier orders in both regimes. Cross-excitation runs mainly from the Quarter-Hourly to the Hourly contract, but this leadership weakens under stress: the ratio of cumulative cross-excitation falls from 2.8 to 1.5, so the two contracts influence each other almost equally. Stress also makes the Quarter-Hourly to Hourly channel much faster, cutting its mean lag from 6.05 to 0.93 seconds. The strong seasonal variation found in calm periods largely disappears under stress, where all four months converge to the same structure.