Pricing and Hedging of Discretely Monitored Asian Options in the Volterra–Heston Model

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Highly relevant for practitioners trading exotic derivatives (Asian options) in commodity, energy, FX, and equity markets. The semi-closed pricing formulas and variance-optimal hedging strategies provide actionable tools for risk management. The control variate approach for arithmetic Asians and the regression-based hedging with geometric controls are directly implementable. The rough volatility framework reflects empirical evidence about volatility dynamics. However, the paper is primarily theoretical/mathematical, and practical implementation requires significant numerical expertise (Riccati-Volterra solvers, Fourier inversion, Markovian lifts).

Very high complexity. Requires solving measure-valued Riccati-Volterra equations, performing Fourier-Laplace contour integration over safe strips, implementing N-factor Markovian lifts with Hausdorff-Bernstein-Widder representations, computing forward-variance curves, implementing GKW decompositions, and running backward regression schemes with ridge regularization. The numerical implementation involves Gauss-Legendre quadrature, Runge-Kutta ODE solvers, exact CIR sampling, trapezoidal variance integration, and common-noise Monte Carlo experiments. Multiple validation checks (constant-variance benchmark, finite-difference hedge verification, equivalence tests) add further complexity.

The paper provides a full computational release with configuration, random seeds, package versions, transform and simulation controls, all replication-level observations, generated tables and figures, and SHA-256 hashes. Source code and full release directory are supplied as ancillary files with the preprint. Quick-mode calculations are explicitly excluded from the evidentiary chain. All numerical parameters, grid sizes, quadrature nodes, and ODE steps are documented.