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

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  • C. F. Lo

Abstract

The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be derived in a straightfoward manner. Time-varying model parameters could also be incorporated into the derivation of the bond price formulae, and this has the added advantage of allowing yield curves to be fitted. Furthermore, the Lie-algebraic approach can be easily extended to formulate new analytically tractable single-factor interest rate models.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnljam:276238
    DOI: 10.1155/2013/276238
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    Cited by:

    1. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    2. Santiago Garcia, 2021. "Group Quantization of Quadratic Hamiltonians in Finance," Papers 2102.05338, arXiv.org, revised Feb 2021.
    3. repec:uts:finphd:40 is not listed on IDEAS
    4. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018, January-A.

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