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Modeling the Term Structure of Interest Rates with General Diffusion Processes: A Moment Approximation Approach

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  • Takamizawa, Hideyuki
  • Shoji, Isao

Abstract

We propose an analytical approximation of the term structure of interest rates under general diffusion processes of the short-rate and state variables. A method of approximating conditional moments as the solution to a system of ordinary differential equations is applied to the pricing of bonds. Numerical experiments based on two illustrative models show that the second-order approximation is accurate for maturities of up to five years and the third-order approximation is effective for longer maturities. We also show the possibility of improving the second-order approximation without much increasing the computational burden.

Suggested Citation

  • Takamizawa, Hideyuki & Shoji, Isao, 2007. "Modeling the Term Structure of Interest Rates with General Diffusion Processes: A Moment Approximation Approach," Discussion Papers 2006-05, Graduate School of Economics, Hitotsubashi University.
  • Handle: RePEc:hit:econdp:2006-05
    Note: This version: October, 2007 (The previous version: October, 2006)
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    References listed on IDEAS

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    1. Pierluigi Balduzzi & Sanjiv Ranjan Das & Silverio Foresi, 1998. "The Central Tendency: A Second Factor In Bond Yields," The Review of Economics and Statistics, MIT Press, vol. 80(1), pages 62-72, February.
    2. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    3. Hideyuki Takamizawa & Isao Shoji, 2004. "On the accuracy of the local linear approximation for the term structure of interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 151-157.
    4. Brenner, Robin J. & Harjes, Richard H. & Kroner, Kenneth F., 1996. "Another Look at Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 85-107, March.
    5. Cheridito, Patrick & Filipovic, Damir & Kimmel, Robert L., 2007. "Market price of risk specifications for affine models: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 83(1), pages 123-170, January.
    6. Knez, Peter J & Litterman, Robert & Scheinkman, Jose Alexandre, 1994. " Explorations into Factors Explaining Money Market Returns," Journal of Finance, American Finance Association, vol. 49(5), pages 1861-1882, December.
    7. Pearson, Neil D & Sun, Tong-Sheng, 1994. " Exploiting the Conditional Density in Estimating the Term Structure: An Application to the Cox, Ingersoll, and Ross Model," Journal of Finance, American Finance Association, vol. 49(4), pages 1279-1304, September.
    8. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    9. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    10. Bali, Turan G., 2000. "Testing the Empirical Performance of Stochastic Volatility Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 35(02), pages 191-215, June.
    11. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
    12. Durham, Garland B., 2003. "Likelihood-based specification analysis of continuous-time models of the short-term interest rate," Journal of Financial Economics, Elsevier, vol. 70(3), pages 463-487, December.
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    Citations

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    Cited by:

    1. TAKAMIZAWA, Hideyuki, 2017. "A Term Structure Model of Interest Rates with Quadratic Volatility," Working Paper Series G-1-18, Center for Financial Research, Graduate School of Commerce and Management, Hitotsubashi University.
    2. Hideyuki Takamizawa, 2015. "Predicting Interest Rate Volatility Using Information on the Yield Curve," International Review of Finance, International Review of Finance Ltd., vol. 15(3), pages 347-386, September.
    3. Takamizawa, Hideyuki, 2015. "Predicting Interest Rate Volatility: Using Information on the Yield Curve," Working Paper Series G-1-9, Center for Financial Research, Graduate School of Commerce and Management, Hitotsubashi University.
    4. Takamizawa, Hideyuki, 2012. "Predicting Interest Rate Volatility: Using Information on the Yield Curve," Working Paper Series G-1-3, Center for Financial Research, Graduate School of Commerce and Management, Hitotsubashi University.
    5. Takamizawa, Hideyuki, 2015. "Impact of No-arbitrage on Interest Rate Dynamics," Working Paper Series G-1-5, Center for Financial Research, Graduate School of Commerce and Management, Hitotsubashi University.

    More about this item

    Keywords

    Short-rate; Term structure; Approximation; Conditional moment;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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