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

Author

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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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    File URL: http://arxiv.org/pdf/2508.14813
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