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Models of Instantaneous Forward Rates

  • Marek Musiela
  • Marek Rutkowski
Chapter
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 36)
The Heath, Jarrow and Morton approach to term structure modelling is based on an exogenous specification of the dynamics of instantaneous, continuously compounded forward rates f(t,T). For any fixed maturity TT*, the dynamics of the forward rate f(t,T) are (cf. Heath et al. (1990a, 1992b))
$$df(t,T)=\alpha (t,T)\,dt+\sigma (t,T)\cdot dW_{t},$$
(1)
where α and σ are adapted stochastic processes with values in ℝ and ℝ d respectively, and W is a d-dimensional standard Brownian motion with respect to the underlying probability measure ℙ (to be interpreted as the actual probability).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Marek Musiela
    • 1
  • Marek Rutkowski
    • 2
  1. 1.BNP ParibasLondonUK
  2. 2.Inst. MathematicsTechnical University WarszawaWarszawaPoland

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