Self- and Mutually-Exciting Processes across the Microstructure Stack

A review of how self- and mutually-exciting point processes are used across high-frequency finance: tick-level volatility estimation, measurement of market endogeneity, systemic contagion, optimal execution, and full order-book dynamics. We use it as the connective reference that places the reflexivity, queue-reactive, and rough-Heston results within one process-level vocabulary.

Multivariate intensity λ^i_t = μ^i + Σ_j ∫ φ_{ij}(t − s) dN^j_s; cross-excitation φ_{ij} encodes lead–lag and contagion, the spectral radius of ∫ Φ governing stability of the system.

The value of the survey for a desk is taxonomic: it makes explicit that volatility, contagion, and momentum are, at the microstructure level, statements about the same kernel matrix viewed through different observables. That discourages treating those memo inputs as independent.

Provides a shared state description across otherwise separate memo sections — microstructure, volatility, and cross-asset transmission can be reasoned about as one excitation structure rather than three.

Most cited applications require venue-level data the desk does not consume directly; the review is integrative rather than prescriptive about estimation under realistic data constraints.