Variance-Optimal Hedging in the Rough Hawkes–Heston Model

Battle Count: 86

Highly relevant for derivatives desk hedging in rough volatility environments. The paper provides explicit formulas for optimal stock positions that account for both Brownian and common marked-jump risks, which is directly applicable to SPX/VIX smile hedging. The convergence results guarantee that practical kernel-regularized strategies approach the theoretical optimum. However, the continuous-time, risk-neutral framework limits direct implementation without adaptation for discrete trading and real-world measures.

Extremely high complexity. Implementation requires: (1) solving Riccati-Volterra integral equations numerically, (2) computing affine conditional transforms with singular kernels, (3) performing Fourier inversion with proper contour selection, (4) constructing predictable memory processes from singular Volterra convolutions, (5) handling common marked jumps in both stock and variance, (6) implementing kernel regularization with proper resolvent computations, and (7) managing the modulus truncation and weighted truncation for convergence guarantees. The numerical simulation itself requires specialized rough-Heston discretization schemes.

The paper provides a GitHub repository with numerical code, detailed calibration parameters from Bondi et al. (2024b), explicit simulation methodology (integrated-variance Euler construction with running-maximum clock), and comprehensive numerical tables with Monte Carlo standard errors. The mathematical proofs are fully self-contained with all assumptions stated. However, the theoretical framework is highly specialized and requires significant expertise in Volterra processes and affine jump-diffusion models to implement independently.