On Inhomogeneous Affine Volterra Processes: Stationarity and Applications to the Volterra Heston Model

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Highly relevant for quantitative trading and derivatives pricing. The Fake Stationary Volterra Heston model provides a tractable framework for option pricing with rough volatility that unifies short- and long-maturity behavior, overcoming a known drawback of classical and rough Heston models. The closed-form characteristic function enables efficient Fourier-based option pricing. The model captures empirically observed roughness in volatility (H<0.5) and long-memory effects (H>0.5). Directly applicable to SPX option pricing, volatility surface calibration, and risk management. However, the theoretical complexity and specialized numerical requirements limit immediate practical deployment.

Very high complexity. Implementation requires: (1) solving inhomogeneous Riccati-Volterra integral equations numerically, (2) computing fractional derivatives and integrals (Riemann-Liouville), (3) evaluating Mittag-Leffler functions and their derivatives, (4) solving the stabilizer functional equation via recursive series expansion, (5) implementing semi-integrated Euler schemes with Cholesky decomposition for correlated Gaussian increments, (6) performing Fourier inversion for option pricing. The mathematical prerequisites include advanced stochastic analysis, fractional calculus, Volterra integral equations, and functional analysis. The paper references specialized numerical schemes (CGP20) for the fractional Riccati equations.

The paper provides detailed mathematical proofs, a semi-integrated Euler-Maruyama scheme for numerical simulation, parameter tables for the Fake Stationary Rough Heston model calibrated to SPX options (from EEGR19), and recursive formulas for computing the stabilizer function. However, no code repository is provided, and the numerical implementation details (Cholesky decomposition for Gaussian vectors, covariance matrix construction) reference external appendices. The theoretical framework is fully self-contained with complete proofs.