On generalized interest rate dynamics

In this paper we consider stochastic interest rate and classify its deterministic part with respect to oscillation and monotonicity, latter according to Kiguradze.We illustrate usefulness of such classification on convenient examples, including feasibility ratio and choice of pension pillar. Interest rate follows a 2nd order quasilinear stochastic differential equation which generalizes a result of [13]. As a side result we obtain Kiguradze characterization of smooth solutions of deterministic part of Parker’s stochastic differential equation. We show that Parker’s model allows oscillations and better long term behavior of the interest rate in comparison of 1st order interest rate model. In such a setup we study the sensitivity of feasibility ratio to the dynamics of the underlying interest rate. We cover the wide spectrum of life time distributions including the generalized Gamma as well as the Gompertz-Makeham law. We apply obtained results to briefly discuss the situation typical for some Eastern-European countries when many people are members of a pension scheme operated under public management as well as a funded scheme financed by employees contributions.