# On a Model for the Term Structure of Interest Rate Processes of Stable Type

### New Zealand Journal of Mathematics

Vol. 38, (2008), Pages 149-160

V. P. Kurenok

Department of Natural and Applied Sciences

University of Wisconsin-Green Bay

2420 Nicolet Drive, Green Bay, WI 54311-7001

United States of America

Abstract Let $M(t), t\ge 0,$ be a one-dimensional symmetric stable process of index $0<\alpha\le 2$. As a model for the term structure of interest rate processes we consider $r(t)={\mathcal G}(t, M\circ T(t))$ where ${\mathcal G}$ and T are some functions. We show that this model includes, in particular, some models which can be described as solutions of Ito stochastic differential equations driven by the process M. We also construct a sequence of simple processes (random walks) which converge in distribution to the interest rate processes r(t).

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Classification (MSC2000)