Modeling the Euro overnight rate

This paper describes the evolution of the daily Euro overnight interest rate (EONIA) by using several models containing the jump component, such as a single-regime ARCH-Poisson–Gaussian process, with either a piecewise function or an autoregressive conditional specification (ARJI) for the jump intensity, and a two-regime-switching process with jumps and time-varying transition probabilities. To model the jump intensity, we include the following effects which are significant for the occurrence of jumps: (1) the end of maintenance period effect because of reserve requirements, (2) the end of month effect, also known as the calendar day effect, caused mainly by accounting adjustments and finally, (3) the meeting effect caused by the meetings of the Governing Council of the European Central Bank (ECB). These effects lead to better performance and several of them are also included for the behavior of the transition probabilities. Since the target of the ECB is to maintain the EONIA rate close to the policy rate, we model the conditional mean of the overnight rate series as a reversion process to this policy rate, distinguishing two alternative speeds of reversion, specifically, a different speed if EONIA is higher or lower than the policy rate. We also study the jumps of the EONIA rate around the ECB's meetings by using the ex-post probabilities of the ARJI model. Finally, we develop a volatility forecasting analysis to measure the performance of the different candidate models.