Heston Pricing Through Affine Group Quantization and Mellin Methods

Summary

The document presents an alternative mathematical framework for pricing options under the Heston stochastic volatility model. It separates the model’s affine pricing symbol into a finite symplectic quadratic component and a complementary holonomy component, then uses a Poincare-Cartan form to derive the characteristic flow associated with the affine Riccati dynamics.

A momentum-based polarization produces a Mellin representation for pricing, and the Riccati equation is also transformed through projective linearization. The proposed pricing formula is checked numerically against the standard Heston solution, and the Black-Scholes model appears as a limiting case. The excerpt describes these mathematical constructions and validation at a high level, but provides no numerical errors, assumptions, or implementation details for assessing practical performance.

Key ideas

• The Heston pricing symbol is split into quadratic and holonomy sectors.
• The characteristic flow of the resulting form yields affine Riccati dynamics.
• Momentum polarization leads to a Mellin-based pricing representation.
• Projective linearization offers another way to handle the Riccati equation.
• The formula is compared numerically with standard Heston pricing, with Black-Scholes recovered as a limit.

Tags

# Group Quantization and Mellin Representations of the Heston Model


# Group Quantization and Mellin Representations of the Heston Model









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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