A volatile foreign exchange market takes a toll on the economy?s international competitiveness. Excess forex volatility affects the stock markets and international trade as well. The negative impact may even spread to other countries in form of volatility spillover. This study aims to analyze the volatility dynamics in context of Indian Rupee vis-a-vis some selected foreign currencies. In that process, it uses ARCH models, long memory and structural breaks to examine the nature of volatility. The study then investigates any possible volatility spillover from stock markets to understand the possible source of exchange rate volatility. However, the stock markets fail to explain the exchange rate volatility completely. To understand the underlying volatility dynamics, the possible non-linear nature of the exchange rates is examined. All exchange rates turn out to be chaotic in nature. It has some serious policy implications as in a chaotic foreign exchange market long term policies are often rendered useless. The study empirically establishes this fact by showing that in chaotic foreign exchange market government interventions to contain volatility does not actually work.