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arXiv · 2606.13992

Group Quantization and Mellin Representations of the Heston Model

Santiago Garcia
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Abstract

We develop an Affine Holonomy Group Quantization framework for the Heston stochastic volatility model. The Heston affine pricing symbol is decomposed into a finite symplectic quadratic sector and a complementary holonomy sector, leading to a Poincare-Cartan form whose characteristic flow yields the affine Riccati dynamics. Momentum polarization gives a Mellin pricing representation, while the Riccati equation admits a projective linearization. The resulting option pricing formula is validated numerically against the standard Heston solution, and the Black-Scholes model is recovered as a limiting case.

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Santiago Garcia. 2026-06-12. Group Quantization and Mellin Representations of the Heston Model. https://arxiv.org/abs/2606.13992

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