This study is an attempt to estimate the dynamics (volatility) of Indian rupee instability against four major world currencies, i.e., US dollar, pound sterling, euro and Japanese yen, using 3,340 daily observations over a period of 13 years from January 3, 2000 to September 30, 2013. This paper uses the Generalized Autoregressive Conditional Heteroskedastic (GARCH) models to estimate volatility (conditional variance) in the daily log rupee value. The models include both symmetric and asymmetric that capture the most common stylized facts about rupee exchange returns such as volatility clustering and leverage effect. It is evident from the findings that asymmetric models are superior to symmetric models in providing a better fit for the exchange rate volatility because of leverage effect.

The currency exchange rates volatility is among the most examined and analyzed economic measures by the government. Recently, India had a big concern about rupee value with respect to US dollar due to its all-time lowest (depreciated) value. On August 28, 2013, the Indian rupee touched up to 68.825 against the dollar. It is not only the rupee depreciation but also rupee appreciation that is causing concern to the economic imbalance of the country. Ahmed and Suliman (2011) pointed out the importance of currency exchange rate volatility because of its economic and financial applications like portfolio optimization, risk management, etc. It is a well-known fact that the exchange rate volatility is not observed directly. A number of models have been developed to get the accurate estimate of the volatility. Out of these, conditional heteroskedastic1 models are frequently used. The foundation for building these models is to make a good forecast of future volatility which would be helpful in obtaining a more efficient portfolio distribution, better foreign exchange exposure management and more accurate currency derivative prices.

Surrounded by these models, the Autoregressive Conditional Heteroskedasticity (ARCH) model proposed by Engle (1982) and its extension, Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model by Bollerslev (1986) and Taylor (1986) are the first models that have become popular in enabling the analysts to estimate the variance of a series at a particular point in time (Enders, 2004). Since then, there have been a great number of empirical applications of modeling the conditional variance of a financial time series (Diebold and Nerlolve, 1989; Nelson, 1991; Bollerslev et al., 1992; West and Cho, 1995; Engle and Patton, 2001; Evans and Lyons, 2002; Shin, 2005; Charles et al., 2008; Jakaria and Abdalla, 2012; and Rossi, 2013). The focus of these studies was to design explicit models to forecast the time-varying volatility of the series using past observations. The findings have been applied successfully in the financial market research.

Applied Finance Journal, Generalized Autoregressive Conditional Heteroskedasticity (GARCH), Exchange Rate, Volatility Estimation, GARCH Models, Autoregressive Conditional Heteroskedasticity (ARCH), Volatility of Exchange Rates, Indian Rupee Against World Currencies.