Limit theorems for Hull-White model with Hawkes jumps

TL;DR

This paper establishes limit theorems such as law of large numbers, central limit theorem, and large deviations for a class of Hull-White models incorporating Hawkes process jumps, aiding long-term interest rate analysis.

Contribution

It introduces new limit theorems for Hull-White models with Hawkes jumps, expanding understanding of their long-term behavior in interest rate modeling.

Findings

Proves law of large numbers for the model

Derives central limit theorem for the model

Establishes large deviations principle

Abstract

In the present paper, we obtain limit theorems for a catogary of Hull-White models with Hawkes jumps including law of large numbers, central limit theorem, and large deviations. In the field of interest rate modeling, it is meaningful in characterizing a long-term rate of return.