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

### From NZJM

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**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 be a one-dimensional symmetric stable process of index . As a model for the term structure of interest rate processes we consider where 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*).

**Keywords**

**Classification** (MSC2000)

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