This dissertation investigates conditional volatility in both spot and futures markets. We examine two approaches in spot market. While A parametric approach is the subject of the second chapter, the third chapter focuses on a nonparametric approach. In futures currency markets, we develop a model to identify the origin of conditional volatility using different type of traders. First, we focus on developing currency markets to explore if the conditional volatility in these markets have characteristics particular to themselves and to what extent these foreign exchange markets (Forex) share the characteristics of the developed markets using parametric models. Therefore, this paper examines weather the statistical models best suited for forecasting volatility of currencies from the high income countries also perform best in forecast of volatility of currencies from emerging market countries. Second, this study aims to forecast the conditional variance of exchange rates in developing countries using a non-parametric kernel smoothing technique with three different kernels: Gaussian, Epanechnikov, and Quartic. The evaluation of the predictive ability based on Root Mean Square Error, Mean Absolute Error, and Mean Absolute Percent Error to forecast 1, 5, and 22 days into the future shows that Gaussian distribution performs the best in short horizon while the other distributions converge to the same outcome as normal distribution in longer horizon. Finally, we try to identify what group of traders (hedgers or speculators) contributes more to the price volatility in currency futures markets. We control for both expected and unexpected trading volume and open interest to estimate the effect of traders' positions on the price volatility of currency futures. We find that short positions have significant associations with the volatility of futures prices. Further, the expected effect of short positions by speculators tends to have a larger effect than the expected effect of short positions by hedgers on volatility while the unexpected effect of short position by hedgers is likely to have a larger effect than the unexpected effect of short positions by speculators.