Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling

TL;DR

The paper introduces the alpha-CIR interest rate model incorporating alpha-stable Levy processes, capturing low interest rates and large jumps in sovereign bond markets through a branching process framework.

Contribution

It extends the standard CIR model by integrating alpha-stable Levy processes and establishes a connection with CBI processes using a novel integral representation.

Findings

Model captures persistency of low interest rates.

Model explains large jumps in sovereign bond markets.

Numerical illustrations demonstrate model behavior.

Abstract

We introduce a class of interest rate models, called the $\alpha$-CIR model, which gives a natural extension of the standard CIR model by adopting the $\alpha$-stable L{\'e}vy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent observations on the sovereign bond market such as the persistency of low interest rate together with the presence of large jumps at local extent. We emphasize on a general integral representation of the model by using random fields, with which we establish the link to the CBI processes and the affine models. Finally we analyze the jump behaviors and in particular the large jumps, and we provide numerical illustrations.