Hawkes processes for credit indices time series analysis: How random are trades arrival times?

Targeting a better understanding of credit market dynamics, the authors have studied a stochastic model named the Hawkes process. Describing trades arrival times, this kind of model allows for the capture of self-excitement and mutual interactions phenomena. The authors propose here a simple yet conclusive method for fitting multidimensional Hawkes processes with exponential kernels, based on a maximum likelihood non-convex optimization. The method was successfully tested on simulated data, then used on new publicly available real trading data for three European credit indices, thus enabling quantification of self-excitement as well as volume impacts or cross indices influences.