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

We develop semi-closed pricing formulas and lifted-model hedging methods for discretely monitored geometric and arithmetic Asian options in the Volterra-Heston stochastic volatility model. Exploiting the affine Volterra structure, we derive a tractable transform for the joint law of the terminal log-price and the discretely monitored geometric average. This transform yields semi-closed pricing formulas for geometric Asian options, which in turn provide effective control variates for Monte Carlo valuation of arithmetic Asian options. Under the stated real-moment and affine-transform hypotheses, we also derive the Galtchouk-Kunita-Watanabe decomposition for Fourier-representable payoffs and obtain a variance-optimal hedge in terms of the Riccati-Volterra equation and the forward-variance curve. Using N-factor Markovian approximations, we obtain a finite-dimensional numerical implementation for hedging Asian options. Our numerical experiments document factor convergence for a regular non-Markovian kernel and the effect of rebalancing frequency on hedging error. In the Heston benchmark, geometric Asian controls substantially reduce the variance of arithmetic-Asian price estimates and improve the finite-sample stability of regression-based hedging relative to direct regression.