  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.
