Affine Pricing Models Based on Group Quantization and Complete Groups

This study proposes the Affine Holonomic Group Quantization (AHGQ) geometric framework, which provides a unified geometric origin for pricing operators in coordinate space and representations of exponential affine transformations for continuous-path, time-homogeneous affine pricing models. The framework decomposes affine pricing symbols into homogeneous quadratic sectors and complementary affine sectors, and validates the approach through Gaussian and square-root models.