The objective of this work is to determine the presence of volatility in the spot and futures exchange rates, detecting, thus, the presence of risk. Identified the volatility, it is looked for shaping it through the construction of models capable to forecast the behavior of the spot and futures exchange rates. The GARCH and TARCH models had been used to shape the volatility of the exchange rates. Gotten the estimates, it is verified existence of convergence of these rates in the date of the expirations of future contracts, identifying, thus, the chance to get profits with arbitrage. The results had shown more that the spot and futures exchange rates are very volatile and the spot exchange market presents asymmetry, being affected for negative impacts. The volatility analysis also indicates that the shocks in these rates last for a long period of time. Finally, it is detected possibility to get profits with arbitrage in the market of Brazilian exchange.