Modeling and forecasting the realized volatility of the eur-dollar exchange rate

Abstract

Consulta en la Biblioteca ETSI Industriales (7805)

[EN] The volatility has become an economic phenomenon studied intensively in recent years for its great importance in decision-making in business, finance or economic policy. The dynamics of the time-varying volatility of financial assets play a main role in diverse fields, such as derivative pricing and risk management. The purpose is to make good decisions in an environment of volatility. To make good decisions, we must have good predictions about the volatility of the variable with which we work. The aim of this paper is to find econometric models that provide volatility appropriate predictions. The most popular method for modelling volatility belongs to the family of GARCH models, although other alternatives (such as stochastic volatility models) also provide reliable estimates. In this paper the models evaluated are the well-known GARCH, FIGARCH and HYGARCH. We also evaluate the FIGARCH and HYGARCH models taking into account the non-negativity constraints. These models are referred to as conditional heteroskedastic models. The success of GARCH processes is unquestionable as they take into account the many observed features of the data, such as thick tails of the distribution, clustering of large and small observations, nonlinearity and changes in our ability to forecast future values. But the volatility of many financial assets also exhibits a strong temporal dependence which is revealed through a slow decay to zero in the autocorrelation function. The basic GARCH model does not succeed in fitting this pattern because it implicitly assumes a fast, geometric decay in the theoretical autocorrelations. For this reason, Integrated models were introduced. These models imply a hyperbolic rate of decay in the autocorrelation function of squared residuals, and generalize the basic framework by still using a parsimonious parameterization. The data set with which we work in is Exchange rate data for Euro / Dollar since December 1, 1998 until October 31, 2006. With the data set, we have calculated different types of returns to find the appropriate model to each return. In this paper we show firstly the Return_Andersen and Return_Andersen_squared, calculated as the sum of the intraday returns with a frequency of 5 minutes. Secondly, Daily returns series and finally evaluating the Realized Volatility series with itself. To generalize results and to be able to find general conclusions, we use three statistical distributions in any evaluation (t-Student, Gaussian and Skewed-Student) and three numbers of steps ahead (1, 15 and 30).