Paper: arXiv 2508.14813

Authors: 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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is highly mathematically dense, featuring infinite-dimensional stochastic partial differential equations, affine processes, operator-valued calculus, and Fourier-based pricing derivations. However, it presents no backtested strategies, implementation details, or statistical validation, focusing instead on theoretical derivations and numerical consistency checks.

Research Flowchart

  flowchart TD
  A["Research Goal: Price options on forwards<br>in function-valued affine SV models"] --> B["Model Selection & Setup<br>HJM-M framework + SPDE dynamics"]
  
  B --> C{"Two Affine SV Class Types"}
  
  C --> D["Model 1: Gaussian<br>Finite-rank Wishart Process"]
  C --> E["Model 2: Pure-Jump<br>Barndorff-Nielsen-Shephard"]

  D --> F["Computational Process:<br>Derive Exponential Moment Conditions"]
  E --> F

  F --> G["Semi-Closed Pricing Formulas<br>via Fourier Transform Methods"]

  G --> H["Key Outcomes:"]
  H --> I["Tractable pricing in<br>infinite-dimensional models"]
  H --> J["Captures maturity-specific<br>and term structure risk"]
  H --> K["Explicit formulas for<br>vanilla calls/puts on forwards"]