New solutions to the bond-pricing equation via Lie's classical method

DOI10.1016/S0895-7177(00)00136-9zbMath0955.91018OpenAlexW2002417392MaRDI QIDQ1585830

Joanna M. Goard

Publication date: 14 November 2000

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0895-7177(00)00136-9

zbMATH Keywords

interest rateLie symmetriesbond-pricing

Mathematics Subject Classification ID

Boundary value problems for linear higher-order PDEs (35G15)

Related Items (16)

Lie-algebraic approach for pricing zero-coupon bonds in single-factor interest rate models ⋮ Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance ⋮ Using Utility Functions to Model Risky Bonds ⋮ Closed-form formulae for European options under three-factor models ⋮ Lie symmetry methods for local volatility models ⋮ Complete Invariant Characterization of Scalar Linear (1+1) Parabolic Equations ⋮ Symmetry-based optimal portfolio for a DC pension plan under a CEV model with power utility ⋮ Ibragimov-type invariants for a system of two linear parabolic equations ⋮ Invariant approach to optimal investment-consumption problem: the constant elasticity of variance (CEV) model ⋮ Invariance properties of a general bond-pricing equation ⋮ Group classification of a general bond-option pricing equation of mathematical finance ⋮ Generalized uncorrelated SABR models with a high degree of symmetry ⋮ Tractable forms of the bond pricing equation ⋮ Two ways to solve, using Lie group analysis, the fundamental valuation equation in the double-square-root model of the term structure ⋮ Optimal portfolio for a defined-contribution pension plan under a constant elasticity of variance model with exponential utility ⋮ Embedding the Vasicek model into the Cox-Ingersoll-Ross model

Cites Work

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• A Theory of the Term Structure of Interest Rates
• Symmetries of Differential Equations: From Sophus Lie to Computer Algebra
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• An equilibrium characterization of the term structure
• Pricing Interest-Rate-Derivative Securities
• Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries

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