The Impact of the Self-Exciting Process on the Short-Term Interest Rate Model

We propose a short-term interest rate model integrating the self-exciting Hawkes process with exogenous jump intensity modeled via the Feller-type square-root process. This framework captures jump clustering while introducing level-dependent variance into jump dynamics. Using stochastic Taylor expansions, we derive closed-form moment solutions and apply GMM estimation. Monte Carlo simulations validate estimator precision. Empirical analysis of US Treasury Bill rates demonstrates enhanced capture of extreme events and clustered jumps, with statistical tests favoring our framework over constant-intensity alternatives. Derivative pricing implications are explored, highlighting the model’s practical relevance in financial markets.