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

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