arXiv:2102.05338

Group Quantization of Quadratic Hamiltonians in Finance

Garcia, Santiago

Published Feb 10, 2021• 1 citation

Abstract

The Group Quantization formalism is a scheme for constructing a functional space that is an irreducible infinite dimensional representation of the Lie algebra belonging to a dynamical symmetry group. We apply this formalism to the construction of functional space and operators for quadratic potentials -- gaussian pricing kernels in finance. We describe the Black-Scholes theory, the Ho-Lee interest rate model and the Euclidean repulsive and attractive oscillators. The symmetry group used in this work has the structure of a principal bundle with base (dynamical) group a semi-direct extension of the Heisenberg-Weyl group by SL(2,R), and structure group (fiber) the positive real line.

DOI: 10.48550/arxiv.2102.05338

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