Multivariate Hawkes Models for High-Frequency Prices and Trades

Summary

This work introduces a multivariate Hawkes point-process model for high-frequency market prices and trading activity. Four interaction kernels represent self-excitation in trade arrivals, mean reversion in price changes, the effect of incoming trades on price moves, and the feedback from price changes to trading activity. Together, these components are designed to capture features such as irregular timing of price moves, discrete price increments, short-horizon mean reversion, and changing correlations across time scales.

The framework also models market impact, including a concave, square-root-like response and its subsequent relaxation. The authors explain that the full impact profile can be estimated from anonymous market data by estimating kernels from empirical conditional mean intensities. They provide numerical examples, real-data applications, and comparisons with earlier approaches. The document describes modeling capabilities and demonstrations, but gives no specific performance results or evidence that estimated impact profiles translate directly into profitable trading strategies.

Key ideas

• The model uses four kernels to represent interactions between trades, price moves, and trading activity.
• It aims to capture high-frequency price patterns, including discrete moves and short-term mean reversion.
• The Hawkes framework models market impact and its relaxation over time.
• Kernel estimates from conditional mean intensities can be used to infer impact profiles from anonymous data.
• The described applications do not establish that the model creates a profitable strategy.

Tags

# Hawkes model for price and trades high-frequency dynamics


# Hawkes model for price and trades high-frequency dynamics









We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by 4 kernels associated with respectively the trade arrival self-excitation, the price changes mean reversion the impact of trade arrivals on price variations and the feedback of price changes on trading activity. It allows one to account for both stylized facts of market prices microstructure (including random time arrival of price moves, discrete price grid, high frequency mean reversion, correlation functions behavior at various time scales) and the stylized facts of market impact (mainly the concave-square-root-like/relaxation characteristic shape of the market impact of a meta-order). Moreover, it allows one to estimate the entire market impact profile from anonymous market data. We show that these kernels can be estimated from the empirical conditional mean intensities. We provide numerical examples, application to real data and comparisons to former approaches.

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