Group Quantization and Mellin Representations of the Heston Model

Santiago Garcia

Papers from arXiv.org

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.

Date: 2026-06, Revised 2026-09
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