Negative interest rates: why and how?

TL;DR

This paper explores the reasons behind negative interest rates, their modeling through second order differential dynamics, and their impact on financial variables like variance and expectations, with practical implications for banking and pensions.

Contribution

It introduces a dynamical framework explaining negative interest rates using second order differential equations, highlighting their effects on financial stability.

Findings

Negative interest rates can arise from second order dynamics.

Negative rates influence the variance and expectation of interest rate processes.

The study discusses practical implications for banking and pension sectors.

Abstract

The interest rates (or nominal yields) can be negative, this is an unavoidable fact which has already been visible during the Great Depression (1929-39). Nowadays we can find negative rates easily by e.g. auditing. Several theoretical and practical ideas how to model and eventually overcome empirical negative rates can be suggested, however, they are far beyond a simple practical realization. In this paper we discuss the dynamical reasons why negative interest rates can happen in the second order differential dynamics and how they can influence the variance and expectation of the interest rate process. Such issues are highly practical, involving e.g. banking sector and pension securities.