Modelling jumps with CARMA(p,q)-Hawkes: An application to corporate bond markets

In this paper, we employ the CARMA(p,q)-Hawkes model to investigate the intraday jumps observed in the corporate bond prices. We introduce a bivariate extension of the model, which deals with the cross-effect of upward and downward price movements. An empirical analysis is conducted on green and brown bonds with analogous characteristics. The findings indicate that higher-order univariate/bivariate CARMA(p,q)-Hawkes models produce a superior fit in jump activity with respect to Hawkes models with exponential kernels.