  We consider a generalization of the Heath Jarrow Morton model for the term
structure of interest rates where the forward rate is driven by Paretian
fluctuations. We derive a generalization of It\^{o}'s lemma for the calculation
of a differential of a Paretian stochastic variable and use it to derive a
Stochastic Differential Equation for the discounted bond price. We show that it
is not possible to choose the parameters of the model to ensure absence of
drift of the discounted bond price. Then we consider a Continuous Time Random
Walk with jumps driven by Paretian random variables and we derive the large
time scaling limit of the jump probability distribution function (pdf). We show
that under certain conditions defined in text the large time scaling limit of
the jump pdf in the Fourier domain is \tilde{omega}_t(k,t) \sim \exp{-K/(\ln(k
t))^2} and is different from the case of a random walk with Gaussian
fluctuations. We also derive the master equation for the jump pdf and discuss
the relation of the master equation to Distributed Order Fractional Diffusion
Equations.
