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Quantitative Finance by Erik Schlogl

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Chapter 8

The Heath/Jarrow/Morton model

Modelling a stochastic evolution of the term structure of interest rates in continuous time initially was based on an “economic equilibrium” approach, beginning with the seminal paper of Vasicek (1977). In that model, continuously compounded interest rates are normally distributed, and thus may become negative with positive probability. Subsequently, the model of Cox, Ingersoll and Ross (1985) guaranteed non-negative interest rates. In both cases, however, the initial term structure of interest rates was a model output, rather than input, making it difficult to fit the model to a term structure currently observed in the market and thus severely limiting the models’ practical usefulness. Hull and White (1990) ...

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