This work aims to seek evidence of risk premium in the option and future foreign exchange markets of dollar in Brazil. For that we used two essays: one that measures the premium for volatility risk in the option market and other which measures the currency risk premium in the future market. In the first case, the premium is estimated as excess return of hedge portfolio. In the second case, the premium is estimated based on risk-adjusted Interest Rate Parity Theory from a CGARCH-M model. There was evidence of forward bias puzzle and premium for volatility and for currency risk both negative and time-varying. The first is responsible for increasing currency option price, while the second is consistent with the mean-variance theory, so risk averse investors required more return when they face higher risk. In addition, unanticipated shocks have an influence in determining the long-term volatility component of currency risk premium. In times of global market uncertainty and increasing liquidity constraints the short-term volatility raises. But only the risk premium can not explain the price biased. So transaction cost and a more effective economic model must be including in futher studies about exchange rate discovering.