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Group Quantization and Mellin Representations of the Heston Model

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  • Santiago Garcia

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.

Suggested Citation

  • Santiago Garcia, 2026. "Group Quantization and Mellin Representations of the Heston Model," Papers 2606.13992, arXiv.org, revised Sep 2026.
    • Handle: RePEc:arx:papers:2606.13992
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    File URL: https://arxiv.org/pdf/2606.13992
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