Long-Term Behaviors of Stochastic Interest Rate Models with Jumps and Memory

TL;DR

This paper investigates the long-term behavior of stochastic interest rate models incorporating jumps and memory, demonstrating convergence properties and analyzing two-factor extensions to understand their asymptotic dynamics.

Contribution

It introduces an extended Cox-Ingersoll-Ross type model with jumps and memory, analyzing its long-term convergence and applying findings to two-factor models.

Findings

Proves convergence of long-term returns in the model.

Characterizes the asymptotic behavior of interest rates with jumps and memory.

Extends analysis to two-factor Cox-Ingersoll-Ross models.

Abstract

In this paper we show the convergence of the long-term return $t^{-\mu}\int_0^tX(s)\d s$ for some $\mu\geq1$, where $X$ is the short-term interest rate which follows an extension of Cox-Ingersoll-Ross type model with jumps and memory, and, as an application, we also investigate the corresponding behavior of two-factor Cox-Ingersoll-Ross model with jumps and memory