Hawkes Processes for Modeling Financial Microstructure Noise

Summary

This work models tick-level asset price changes using marked point processes with self-exciting and mutually exciting Hawkes intensities. Separate counting processes represent positive and negative price jumps. By coupling the upward and downward event intensities across one asset or a pair of assets, the model captures short-horizon mean reversion and the Epps effect, in which return correlations weaken at fine time scales, while retaining Brownian-like behavior at longer horizons.

The authors derive closed-form expressions for the mean signature plot and for correlations between two price increments, allowing the scale-dependent transition from mean reversion to diffusion to be studied analytically. They report that theoretical results are consistent with empirical fits to Euro-Bund and Euro-Bobl futures in several settings. The excerpt does not give the fitting details or establish that the model generalizes beyond these contracts and situations.

Key ideas

• The model represents upward and downward price jumps with marked counting processes.
• Self-exciting and mutually exciting Hawkes intensities link price events within and across assets.
• Coupled intensities reproduce short-term mean reversion and the Epps effect.
• Closed-form results describe signature plots and cross-asset increment correlations across time scales.
• Empirical fits are reported for Euro-Bund and Euro-Bobl futures.

Tags

# Modeling microstructure noise with mutually exciting point processes


# Modeling microstructure noise with mutually exciting point processes









We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self and mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process with the positive and negative jumps of an asset price. By coupling suitably the stochastic intensities of upward and downward changes of prices for several assets simultaneously, we can reproduce microstructure noise (i.e. strong microscopic mean reversion at the level of seconds to a few minutes) and the Epps effect (i.e. the decorrelation of the increments in microscopic scales) while preserving a standard Brownian diffusion behaviour on large scales. More effectively, we obtain analytical closed-form formulae for the mean signature plot and the correlation of two price increments that enable to track across scales the effect of the mean-reversion up to the diffusive limit of the model. We show that the theoretical results are consistent with empirical fits on futures Euro-Bund and Euro-Bobl in several situations.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.