Expanding the Rough Heston Model in H

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Directly relevant to quantitative trading in equity derivatives. The rough Heston model is one of the most established frameworks for equity volatility modeling. The paper provides an efficient numerical method for pricing European options across a range of Hurst parameters, which is critical for calibration, hedging, and trading strategies. The ability to compute prices for many H values from a single reference solution is particularly valuable for model calibration and sensitivity analysis in trading desks.

The theoretical framework involves fractional calculus, Volterra integral equations, Bell polynomials, and polygamma functions. The numerical implementation requires solving linear Volterra equations with fractional-logarithmic kernels via product integration, handling complex-valued Riccati equations, and implementing Fourier pricing with adaptive contour cutoffs. However, the authors provide open-source code and the expansion computation itself reduces to matrix multiplications once the reference solution is available. The classical Heston case (H0=1/2) simplifies to standard ODEs.

Full code for numerical experiments is available on GitHub (https://github.com/hagerpa/roughprix). Model parameters are explicitly stated. The implementation uses JAX on Apple M3 CPU. However, reproducing the full theoretical proofs and all numerical benchmarks requires significant expertise in fractional calculus and Volterra equations.