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A two‐mean reverting‐factor model of the term structure of interest rates

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  • Manuel Moreno

Abstract

This article presents a two‐factor model of the term structure of interest rates. It is assumed that default‐free discount bond prices are determined by the time to maturity and two factors, the long‐term interest rate, and the spread (i.e., the difference) between the short‐term (instantaneous) risk‐free rate of interest and the long‐term rate. Assuming that both factors follow a joint Ornstein‐Uhlenbeck process, a general bond pricing equation is derived. Closed‐form expressions for prices of bonds and interest rate derivatives are obtained. The analytical formula for derivatives is applied to price European options on discount bonds and more complex types of options. Finally, empirical evidence of the model's performance in comparison with an alternative two‐factor (Vasicek‐CIR) model is presented. The findings show that both models exhibit a similar behavior for the shortest maturities. However, importantly, the results demonstrate that modeling the volatility in the long‐term rate process can help to fit the observed data, and can improve the prediction of the future movements in medium‐ and long‐term interest rates. So it is not so clear which is the best model to be used. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23: 1075–1105, 2003

Suggested Citation

  • Manuel Moreno, 2003. "A two‐mean reverting‐factor model of the term structure of interest rates," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(11), pages 1075-1105, November.
  • Handle: RePEc:wly:jfutmk:v:23:y:2003:i:11:p:1075-1105
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    Cited by:

    1. Lourdes Gómez-Valle & Julia Martínez-Rodríguez, 2010. "Improving the term structure of interest rates: two-factor models," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 15(3), pages 275-287.
    2. Fernando Rubio, 2004. "Eficiencia Simple Del Mercado De Renta Fija En Chile," Finance 0405009, University Library of Munich, Germany.
    3. Tarik Bazgour & Federico Platania, 2022. "A defaultable bond model with cyclical fluctuations in the spread process," Annals of Operations Research, Springer, vol. 312(2), pages 647-672, May.

    More about this item

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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