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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, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:276238
    DOI: 10.1155/2013/276238
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    References listed on IDEAS

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    1. C. F. Lo & C. H. Hui, 2002. "Pricing multi-asset financial derivatives with time-dependent parameters—Lie algebraic approach," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 32, pages 1-10, January.
    2. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Longstaff, Francis A., 1989. "A nonlinear general equilibrium model of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 23(2), pages 195-224, August.
    5. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    6. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    7. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
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