An E-ARCH Model for the Term-Structure of Implied Volatility

We construct a statistical model for the termstructure of implied volatilities of currency options based on daily historical data for currency pairs over a month period We examine the joint evolution of month month month month and year atthemoney options in all the currency pairs We show that there exist three uncorrelated state variables principal components which account for the parallel movement slope oscillation and curvature of the term structure and which explain on average the movements of the termstructure of volatility to more than in all cases We test and construct an exponential ARCH or EARCH model for each state variable One of the applications of this model is to produce condence bands for the term structure of volatilit