Lie-Algebraic Approach for Pricing Zero-Coupon Bonds in Single-Factor Interest Rate Models

Lo, Chi‐Fai

doi:10.1155/2013/276238

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…The group law (11) provides a coordinate representation 11 of the abstract operators P, Q and 1 acting on the functional 8 The action of W on sl(2, R is…”

Section: Lagrangianmentioning

confidence: 99%

Group Quantization of Quadratic Hamiltonians in Finance

Garcia

2021

Preprint

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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) R + . By using a R + central extension, we obtain the appropriate commutator between the momentum and coordinate operators [ p, x] = 1 from the beginning, rather than the quantum-mechanical [ p, x] = −i . The integral transformation between momentum and coordinate representations is the bilateral Laplace transform, an integral transform associated to the symmetry group.

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“…The group law (11) provides a coordinate representation 11 of the abstract operators P, Q and 1 acting on the functional 8 The action of W on sl(2, R is…”

Section: Lagrangianmentioning

confidence: 99%

Group Quantization of Quadratic Hamiltonians in Finance

Garcia

2021

Preprint

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European call option issued on a bond governed by a geometric or a fractional geometric Ornstein-Uhlenbeck process

Mishura¹,

Rizhniak²,

Zubchenko³

2014

Modern Stoch. Theory Appl.

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European call option issued on a bond governed by a modified geometric Ornstein-Uhlenbeck process, is investigated. Objective price of such option as a function of the mean and the variance of a geometric Ornstein-Uhlenbeck process is studied. It is proved that the "Ornstein-Uhlenbeck" market is arbitrage-free and complete. We obtain risk-neutral measure and calculate the fair price of a call option. We consider also the bond price, governed by a modified fractional geometric Ornstein-Uhlenbeck process with Hurst index ∈ (1/2, 1). Limit behaviour of the variance of the process as → 1/2 and → 1 is studied, the monotonicity of the variance and the objective price of the option as a function of Hurst index is established.

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