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On a general class of one-factor models for the term structure of interest rates (*)


  • W.M. Schmidt

    () (Deutsche Morgan Grenfell, Global Markets, OTC-Derivate, D-60325 Frankfurt am Main, Germany)


We propose a general one-factor model for the term structure of interest rates which based upon a model for the short rate. The dynamics of the short rate is described by an appropriate function of a time-changed Wiener process. The model allows for perfect fitting of given term structure of interest rates and volatilities, as well as for mean reversion. Moreover, every type of distribution of the short rate can be achieved, in particular, the distribution can be concentrated on an interval. The model includes several popular models such as the generalized Vasicek (or Hull-White) model, the Black-Derman-Toy, Black-Karasinski model, and others. There is a unified numerical approach to the general model based on a simple lattice approximation which, in particular, can be chosen as a binomial or $N$-nomial lattice with branching probabilities $1/N$.

Suggested Citation

  • W.M. Schmidt, 1996. "On a general class of one-factor models for the term structure of interest rates (*)," Finance and Stochastics, Springer, vol. 1(1), pages 3-24.
  • Handle: RePEc:spr:finsto:v:1:y:1996:i:1:p:3-24
    Note: received: May 1995; final revision received: June 1996

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    References listed on IDEAS

    1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
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    More about this item


    Term structure of interest rates; contingent claim pricing; lattice approximation;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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