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

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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 $M(t), t\ge 0,$ 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 $r (t)$ .