Modeling Forex Returns Volatility : A Random Level Shift Model with Varying Jump Probability and Mean Reversion . The Case of Latin America

We use a basic random level s fts (RLS) with time varying probabilities and mean reversion mechanism to model the Forex returns volatility in six Latin American Forex Markets: Argentina, Brazil, Chile, Colombia, Mexico and Peru. The results reveal that since the level shifts are taken into account, the long-memory presence dissapears in the autocorrelation function of the volatility series. Furthermore, evidence of conditional hetercedasticity is also removed. KeyWords: Random Level Shifts, Long memory, Forex Returns Volatility, Latin american Forex Markets, Time Varying probability, Mean-Reversion. JEl Classi cation: C22, C51, C53 Address for Correspondence: Gabriel Rodríguez, Department of Economics, Ponti cia Universidad Católica del Perú, Av. Universitaria 1801, Lima 32, Lima, Perú, Telephone: +511-626-2000 (4998), Fax: +511-626-2874. E-Mail Address: gabriel.rodriguez@pucp.edu. pe. 1 Introduction There is a concise conclusion saying that nancial asset returns in high frequency (as daily or monthly) are almost unpredictable. However, their volatilities sure they arent. This implies great disposition to acquire great knowledge for nancial economics, risk management (Bollerslev, Engle, and Nelson (1994)) and for the pricing of primary and derivative assets (Engle and Ng (1993)). We know, evidently, that volatility is unobservable and the literature has worked to get this variable either by tting parametric econometric models such as GARCH, by studying volatility implied by option prices in conjunction with option pricing models such as Black and Scholes (1976), by modeling a stochastic volatility model or by extracting it with absolute or squared returns. Each path has its weaknesses. However, we are going to take the last form, extracting the volatility with absolute returns and form a model with this variable. Volatility, simply de ning, measures the dispersion of an asset price returns. Forex returns volatility is important for any economic agent in the world, such as for academics, policymakers, regulators, market practitioners, etc. Volatility is the one that could tell us about how news a¤ects asset prices, what information is considerably important, and nally how markets process that information. Policymakers are concerned in measuring volatility of asset prices to get an idea of how markets respond to uncertainty and form its expectations. Latin American countries are now concerned with Forex volatilities because of the tremendous impact of the quantitative easing applied from the U.S. Others, as well as regulators or even traders and foreign investors, must take into account not only the expected return of their trading (portfolio, for investors) strategy, but also the exposure of their transactions to risk during periods of high volatility. Tradersnegotiations will have a good performance depending upon the accuracy of their volatility predictions. In summary, economic agents use volatility predictions as an important instrument for risk management. In nancial econometrics, the literature has grown considerably through many years and many authors have tried to debate constantly about which model describes better this variable and, obviously, making good forecast performance. First of all, we have to go back to 1982, in economics literature when scienti c research done by Nelson and Plosser (1982) showed that GDP had in its autocorrelation function a slow decay, which they interpreted, with econometric results, as an conclusive evidence of a unit root. However, Perron (1989) proposed an intriguing argument saying that unit roots are confused with structural breaks. This implied that models explaining long memory are not necessarily the best ones to capture the real Data Generating Process. Even though this conclusion had a tremendous impact in econometric literature, it was much later when this concern was placed in nancial econometrics. The eld of econometrics has had an evolution that could be divided in three stages. In the rst stage, between the 80s and 90s, attention was focused between the ARMA model, then the ARFIMA (Hosking (1981)) and nally we got into the FIGARCH model (Baillie et al (1996)) where the volatility was modeled with a fractional integrated GARCH. All these models imply long memory in the series autocorrelation functions and the forecasts were made according to this fact. In the second stage, between 1997 and 2009, a timid but a great concern arised starting with Teverovsky and Taqqu (1997) who argued something that Perron (1989) questioned in economic variables: structural changes could be confused with long memory. These years saw the concern rised also with Grourieroux and Jasiak (2001), Diebold and Inoue (2001), Granger and Hyung (2004) and others.