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Group Quantization of Quadratic Hamiltonians in Finance

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  • Santiago Garcia

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.

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  • Santiago Garcia, 2021. "Group Quantization of Quadratic Hamiltonians in Finance," Papers 2102.05338, arXiv.org, revised Feb 2021.
    • Handle: RePEc:arx:papers:2102.05338
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    References listed on IDEAS

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    1. C. F. Lo, 2013. "Lie-Algebraic Approach for Pricing Zero-Coupon Bonds in Single-Factor Interest Rate Models," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, May.
    2. Peter Carr & Robert Jarrow & Ravi Myneni, 2008. "Alternative Characterizations Of American Put Options," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 5, pages 85-103, World Scientific Publishing Co. Pte. Ltd..
    3. A. Paliathanasis & R. M. Morris & P. G. L. Leach, 2016. "Lie symmetries of (1+2) nonautonomous evolution equations in Financial Mathematics," Papers 1605.01071, arXiv.org.
    4. T. K. Jana & P. Roy, 2011. "Pseudo Hermitian formulation of Black-Scholes equation," Papers 1112.3217, arXiv.org.
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