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Pricing and Hedging of Discretely Monitored Asian Options in the Volterra-Heston Model — arXiv:2609.07169

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.07169
License (as archived): CC0-1.0
Archived: 2026-10-16T14:35:31.872Z
SHA-256 of the archived text: df63e9df1366e85ecc52b46b5b44920ad7108e2259900cfc6759b44022d55ccc
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How to cite

Pricing and Hedging of Discretely Monitored Asian Options in the Volterra-Heston Model — arXiv:2609.07169 — arXiv (en), https://arxiv.org/abs/2609.07169 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_4f000efcd63d (Metraipolis archive dc_4f000efcd63d, sha256 df63e9df1366e85ecc52b46b5b44920ad7108e2259900cfc6759b44022d55ccc)

BibTeX

@misc{dc4f000efcd63d,
  title = {Pricing and Hedging of Discretely Monitored Asian Options in the Volterra-Heston Model — arXiv:2609.07169},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.07169},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_4f000efcd63d; sha256 df63e9df1366e85ecc52b46b5b44920ad7108e2259900cfc6759b44022d55ccc},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.07169. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-09 in math.PR).
Categorie arXiv: Pricing of Securities (q-fin.PR) ; Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.07169 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T14:09:59.845Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).