This study investigates models for overnight interest rate volatility in Turkey and USA using the Asymmetric GARCH models and determines the best forecasting volatility models. These models are then completed with the use of out of sample forecasting. The best forecasting volatility models were chosen as the best forecasting is done with taking importance of the choosing criteria. First of all, for purposes of assessing volatility, the monthly data were used to investigate the leverage effect and features of fat tail for the period between 2000.01 and 2011.06. Student-t, GED and normal distributions are mentioned with GARCH models, which reflect the symmetric movements; and the EGARCH, GJR-GARCH, Asymmetric PARCH A-CGARCH are used for the asymmetric movements. The models are estimated for the period between 2000.01 and 2011.06, and models are evaluated for out of sample forecasting for the period between 2011.08 and 2012.01. The best forecasting models are determined in these estimated models, following which the best forecasting models are estimated for five months until 2012.01. These forecastings are compared with the volatility for same real period, and the models forecastings were evaluated. The asymmetric and leverage effects are seen in the estimation results.