Multivariate Quadratic Hawkes Processes – Part II: Non-Parametric Empirical Calibration

Battle Count: 85

Highly relevant for quantitative trading in several ways: (1) Provides interpretable feedback mechanisms for volatility dynamics across assets, crucial for risk management and position sizing. (2) Identifies cross-asset volatility spillovers (e-mini to other futures, market factor to stock residuals) that inform hedging strategies. (3) The cross-Zumbach and cross-leverage effects discovered here are new stylized facts that can be exploited in multi-asset trading strategies. (4) The near-criticality finding (endogeneity ratios >0.95) has implications for systemic risk and market stability. (5) The factor model calibration for 317 stocks provides a framework for understanding idiosyncratic vs. systematic volatility dynamics. However, the model is primarily descriptive/diagnostic rather than directly predictive of returns.

High implementation complexity due to: (1) Multi-step calibration procedure requiring careful sequencing (4 steps with dependencies). (2) Construction of large Yule-Walker linear systems with tensor structures (4q²+6q unknowns for lag q). (3) Data preprocessing pipeline including normalization, intraday seasonality removal, and martingalisation. (4) Noise reduction through parametric fitting of covariance structures and rank-one approximations. (5) Symmetrization of data to separate leverage from quadratic effects. (6) Handling of non-symmetric cross-kernels requiring separate treatment of τ1<τ2 and τ1>τ2. (7) Choice of truncation lag q and its impact on stability. The mathematical framework is well-specified but requires careful numerical implementation.

The methodology is described in extensive detail including Yule-Walker equations, calibration matrices, and synthetic data proofs of concept (Appendix A). However, the empirical data (1-minute OHLC for 6 futures and 317 S&P500 stocks, 2013-2023) is proprietary (Capital Fund Management). The calibration procedure is fully specified with equations and algorithmic steps, making the method reproducible given access to similar data. No code repository is mentioned.