Group Quantization and Mellin Representations of the Heston Model

Battle Count: 69

The paper is primarily a theoretical contribution to mathematical finance, providing a geometric reformulation of the Heston model. While it does not directly propose trading strategies or signal generation methods, it offers a deeper structural understanding of stochastic volatility pricing. The Mellin-projective pricing formula is equivalent to existing semi-analytic methods, so it does not provide new computational tools for real-time trading. However, the geometric framework could inspire new approaches to model calibration, risk decomposition, or extension to more complex derivative products. The relevance is more foundational/academic than directly actionable for quantitative trading desks.

The paper requires advanced knowledge of differential geometry, symplectic geometry, Lie group theory, central extensions, groupoids, holonomy, and geometric quantization. The AHGQ construction involves: (1) decomposing the affine pricing symbol into quadratic and complementary sectors, (2) constructing a centrally extended symplectic Lie group, (3) computing left- and right-invariant generators, (4) deriving the Poincaré-Cartan form and characteristic field, (5) performing spatial polarizations, (6) applying Mellin transformation, and (7) solving the projective Riccati system. The numerical implementation requires careful handling of complex logarithm branches along the Mellin contour and avoiding poles of the Riccati solution. This is far more complex than standard Heston pricing implementations.

The paper provides explicit closed-form expressions for the Riccati characteristic D(τ,q) and affine amplitude A(τ,q), along with detailed derivations in appendices. Numerical validation is performed against the standard semi-analytic Heston formula with specified baseline parameters. However, no code repository or implementation code is provided. The mathematical framework is fully self-contained with all formulas explicitly stated, enabling independent reproduction of the numerical tests. The continuous branch selection of log E_τ(q) along the Mellin contour is described but implementation details are limited.