A model for interest rates with clustering effects

We propose a model for short-term rates driven by a self-exciting jump process to reproduce the clustering of shocks on the Euro overnight index average (EONIA). The key element of the model is the feedback effect between the absolute value of jumps and the intensity of their arrival process. In this setting, we obtain a closed-form solution for the characteristic function for interest rates and their integral. We introduce a class of equivalent measures under which the features of the process are preserved. We infer the prices of bonds and their dynamics under a risk-neutral measure. The question of derivatives pricing is developed under a forward measure, and a numerical algorithm is proposed to evaluate caplets and floorlets. The model is fitted to EONIA rates from 2004 to 2014 using a peaks-over-threshold procedure. From observation of swap curves over the same period, we filter the evolution of risk premiums for Brownian and jump components. Finally, we analyse the sensitivity of implied caplet volatility to parameters defining the level of self-excitation.