Limit theorems for Hull-White model with Hawkes jumps

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.

There is a fundamental flaw in this paper. The positivity of the process can't be guaranteed. As a result, the intensity of the jumps may be meaningless