A model for interest rates with clustering effects

Donatien Hainaut (1)

1 ESC [Rennes] - ESC Rennes School of Business

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 eect 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 oorlets. The model is tted to EONIA rates from 2004 to 2014 using a peaks-over-threshold procedure. From observation of swap curves over the same period, we lter the evolution of risk premiums for Brownian and jump components. Finally, we analyze the sensitivity of implied caplet volatility to parameters dening the level of self-excitation.

Mots clés: Hawkes process; Self-exciting process; Yield curve; Interest rates

Domaines: Economies et finances

Donatien Hainaut. A model for interest rates with clustering effects. Quantitative Finance, 2016, Vol. 16 (Issue 8), pp. 1203-1218. ⟨10.1080/14697688.2015.1135251⟩. ⟨hal-01393994⟩