Exchange rates and other kinds of traded financial functions such as interest rates, stock prices are prone to constant variability. This variability influences the flow of goods, services, and capital in a country, and exerts strong pressure on the balance of payments, inflation and other macroeconomic variables. Particularly, the exchange rate of Naira in relation to many other currencies of the world fluctuate such that their returns over different periods of time are significantly volatile and difficult to forecast. This problem of exchange rate variability have become too disturbing, thus the need to model this fluctuation. The empirical evidence provided in this study uses ARCH and GARCH models for modelling this variability in rate as they are found to capture the “stylised facts” of financial returns such as: leptokurtosis, volatility clustering, intermittency, fat tails, leverage effect etc. As such, this book comes handy as it could be employed in assessing the condition of the financial markets for making decisions by investors, speculators, investment managers and financial regulators, both in a developed and a developing economy.