Pricing and Hedging of Discretely Monitored Asian Options in the Volterra-Heston Model
Abstract
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.
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BibTeX
@misc{custers2026pricing,
title = {{Pricing and Hedging of Discretely Monitored Asian Options in the Volterra-Heston Model}},
author = {Gijs Custers and Sven Karbach and Martin Friesen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07169},
eprint = {2609.07169},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07169},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pricing and Hedging of Discretely Monitored Asian Options in the Volterra-Heston Model
AU - Gijs Custers
AU - Sven Karbach
AU - Martin Friesen
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07169
UR - https://arxiv.org/abs/2609.07169
AB - 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.
ER -