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Pricing Options on Forwards in Function-Valued Affine Stochastic Volatility Models

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  • Jian He
  • Sven Karbach
  • Asma Khedher

Abstract

We study the pricing of European-style options written on forward contracts within function-valued infinite-dimensional affine stochastic volatility models. The dynamics of the underlying forward price curves are modeled within the Heath-Jarrow-Morton-Musiela framework as solution to a stochastic partial differential equation modulated by a stochastic volatility process. We analyze two classes of affine stochastic volatility models: (i) a Gaussian model governed by a finite-rank Wishart process, and (ii) a pure-jump affine model extending the Barndorff--Nielsen--Shephard framework with state-dependent jumps in the covariance component. For both models, we derive conditions for the existence of exponential moments and develop semi-closed Fourier-based pricing formulas for vanilla call and put options written on forward price curves. Our approach allows for tractable pricing in models with infinitely many risk factors, thereby capturing maturity-specific and term structure risk essential in forward markets.

Suggested Citation

  • Jian He & Sven Karbach & Asma Khedher, 2025. "Pricing Options on Forwards in Function-Valued Affine Stochastic Volatility Models," Papers 2508.14813, arXiv.org.
    • Handle: RePEc:arx:papers:2508.14813
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    References listed on IDEAS

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    1. Cox, Sonja & Karbach, Sven & Khedher, Asma, 2022. "Affine pure-jump processes on positive Hilbert–Schmidt operators," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 191-229.
    2. Fred Espen Benth & Jūratė Šaltytė Benth, 2012. "Modeling and Pricing in Financial Markets for Weather Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8457, April.
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    4. repec:eme:mfppss:03074350510769703 is not listed on IDEAS
    5. Sven Karbach, 2024. "Heat modulated affine stochastic volatility models for forward curve dynamics," Papers 2409.13070, arXiv.org.
    6. Fred Espen Benth & Carlo Sgarra, 2024. "A Barndorff-Nielsen and Shephard model with leverage in Hilbert space for commodity forward markets," Finance and Stochastics, Springer, vol. 28(4), pages 1035-1076, October.
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    11. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    12. René A. Carmona & Michael R. Tehranchi, 2006. "Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective," Springer Finance, Springer, number 978-3-540-27067-6, October.
    13. Dennis Schroers, 2024. "Dynamically Consistent Analysis of Realized Covariations in Term Structure Models," Papers 2406.19412, arXiv.org.
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