Microstructural Foundation for the Rough Hawkes–Heston Model

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Highly relevant for quantitative trading in derivatives markets. The rough Hawkes-Heston model with common jumps is directly applicable to SPX/VIX option pricing, volatility surface calibration, and risk management. The microstructural foundation provides economic justification for model parameters and helps understand the origin of leverage, roughness, and jump clustering. The affine Volterra structure preserves tractability for pricing and hedging. However, the paper is primarily theoretical and does not provide trading strategies or execution algorithms directly.

Extremely high complexity. The paper involves: (1) construction of a Poisson-embedded marked Hawkes system with two-sign balance, (2) near-critical resolvent asymptotics with Mittag-Leffler kernels, (3) fractional rewriting via Riemann-Liouville calculus, (4) joint tightness and noise identification in a common filtration, (5) complete weak uniqueness via Girsanov arguments, (6) singular Volterra stochastic convolution convergence, and (7) time-simplicity proofs for jump measures. Numerical implementation requires exact immigration-branching simulation, affine Riccati-Volterra transforms with exponential kernel decomposition, and COS method for option pricing.

The paper provides explicit parameter values for numerical experiments (Section 6) including alpha=0.65, mu_0=1, theta=0.2, c_J=0.4, r_star=1.25, and the Bondi et al. (2024b) calibration parameters. The exact immigration-branching representation is specified. However, the theoretical proofs are highly complex and the code is not publicly available. The numerical experiments use 100,000 Monte Carlo paths and deterministic affine-transform inversion, which are reproducible given the stated parameters.