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Pricing of geometric Asian options in the Volterra-Heston model

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  • Florian Aichinger
  • Sascha Desmettre

Abstract

Geometric Asian options are a type of options where the payoff depends on the geometric mean of the underlying asset over a certain period of time. This paper is concerned with the pricing of such options for the class of Volterra-Heston models, covering the rough Heston model. We are able to derive semi-closed formulas for the prices of geometric Asian options with fixed and floating strikes for this class of stochastic volatility models. These formulas require the explicit calculation of the conditional joint Fourier transform of the logarithm of the stock price and the logarithm of the geometric mean of the stock price over time. Linking our problem to the theory of affine Volterra processes, we find a representation of this Fourier transform as a suitably constructed stochastic exponential, which depends on the solution of a Riccati-Volterra equation. Finally we provide a numerical study for our results in the rough Heston model.

Suggested Citation

  • Florian Aichinger & Sascha Desmettre, 2024. "Pricing of geometric Asian options in the Volterra-Heston model," Papers 2402.15828, arXiv.org, revised Jul 2024.
    • Handle: RePEc:arx:papers:2402.15828
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    References listed on IDEAS

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    1. Eduardo Abi Jaber & Enzo Miller & Huy^en Pham, 2020. "Markowitz portfolio selection for multivariate affine and quadratic Volterra models," Papers 2006.13539, arXiv.org, revised Jan 2021.
    2. Jim Gatheral & Martin Keller-Ressel, 2019. "Affine forward variance models," Finance and Stochastics, Springer, vol. 23(3), pages 501-533, July.
    3. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. Paul Glasserman & Pu He, 2020. "Buy rough, sell smooth," Quantitative Finance, Taylor & Francis Journals, vol. 20(3), pages 363-378, March.
    6. Omar El Euch & Mathieu Rosenbaum, 2019. "The characteristic function of rough Heston models," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 3-38, January.
    7. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
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