Endogeneity Near Criticality in Self-Exciting Mid-Price Dynamics

Modelling E-mini S&P mid-price changes as a self-exciting Hawkes process, the authors estimate a power-law kernel whose branching ratio sits very close to unity throughout 1998–2011, implying markets are persistently near-critical: most activity is endogenously generated rather than driven by exogenous news. The kernel integrates to one independently of period, so endogeneity has not so much increased as accelerated.

Intensity λ_t = μ + Σ_{t_i < t} φ(t − t_i) with kernel φ(τ) ∝ τ^{−(1+β)} and branching ratio n = ∫ φ → 1⁻; the exogenous fraction of activity is (1 − n).

The near-critical estimate is the headline, but the durable lesson is methodological: with n ≈ 1 the response to a genuine exogenous shock is amplified by a long cascade, so the same news produces very different paths depending on the prevailing endogeneity. We read high estimated n as a regime in which apparent momentum is mechanically, not informationally, supported.

Near-critical regimes are ambiguity-rich. Signal classifications issued into such regimes should carry lower conditional confidence and lean on reconciled fundamental evidence rather than on price continuation.

Branching-ratio estimates are sensitive to kernel parameterization, event-time aggregation, and treatment of self-trades; the bias generally inflates n toward one.