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We employ MIDAS (Mixed Data Sampling) to study the risk-expected return trade-off in several European stock indices. Using MIDAS, we report that, in most indices, there is a significant and positive relationship between risk and expected return. This strongly contrasts with the result we obtain when we employ both symmetric and asymmetric GARCH models for conditional variance. We also find that asymmetric specifications of the variance process within the MIDAS framework improve the relationship between risk and expected return. Finally, we introduce bivariate MIDAS and find some evidence of significant pricing of the hedging component for the intertemporal riskreturn trade-off.3

The term structure of interest rates is an instrument that gives us the necessary information for valuing deterministic financial cash flows, measuring the economic market expectations and testing the effectiveness of monetary policy decisions. However, it is not directly observable and needs to be measured by smoothing data obtained from asset prices through statistical techniques. Adjusting parsimonious functional forms -as proposed by Nelson and Siegel (1987) and Svensson (1994) -is the most popular technique. This method is based on bond yields to maturity and the high degree of non-linearity of the functions to be optimised make it very sensitive to the initial values employed. In this context, this paper proposes the use of genetic algorithms to find these values and reduce the risk of false convergence, showing that stable time series parameters are obtained without the need to impose any kind of restrictions.

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 such as: (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 the accounting adjustments and finally, (3) the meeting effect caused by the fortnightly meetings of the Governing Council of the European Central Bank (ECB). These effects lead to a better performance and several of them are also included for the behavior of the transition probabilities. Since the target of the ECB is keeping the EONIA rate close to the official rate, we have modeled the conditional mean of the overnight rate series as a reversion process to the official rate distinguishing two alternative speeds of reversion, in concrete, a different speed if EONIA is higher or lower than the official 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 an out-of-sample forecasting analysis to measure the performance of the different candidate models.JEL classification: C13, C22, E43, E52.