9th Symposium on Finance, Banking, and Insurance
Universität Karlsruhe (TH), Germany, December 11 - 13, 2002

Abstract

ON A MODEL FOR THE TERM STRUCTURE OF INTEREST RATE PROCESSES OF STABLE TYPE

W. P. Kurenok

Department of Mathematics and Mechanics
Belorussian State University

Let M(t), t > 0 be an arbitrary one-dimensional symmetric stable process. As a model for the term structure of interest rate processes we consider r(t) = G(t, M(T(t))) or as special case r(t) = F (f(t) + g(t)M(T(t))) for some functions G, F, T, f and g. We show that this model includes in particular some models which can be described by the Ito stochastic differential equations driven by the stable process M. It generalizes also the known Schmidt's model which is the special case of our model. Moreover, we construct also a sequence of more simple processes (random walks) obtained as the sums of i.i.d random variables which belong to the domain of attraction of the corresponding stable distribution. It is proved that this random walk models converge in the distribution law to the interest rate processes r(t).