Asymmetric Nonlinear Smooth Transition Garch Models

Abstract

Many studies of time varying volatility in stock markets have focused on an asymmetry in the volatility process known as “the leverage effect.” This asymmetry, first noted by Black in 1976, is characterized by the market’s asymmetric reaction to news, in the sense that stock market returns become more volatile after a negative price shock, than they do after a positive shock of the same absolute size. The first empirical models which explicitly attempted to capture the leverage effect include Engle’s (1990) A-GARCH model, Nelson’s (1991) E-GARCH model, and then the switching GARCH model proposed by Glosten, et al. (1993). Nowadays, there are many models which attempt to incorporate this asymmetry,1 and they are often conveniently summarized and compared using Engle and Ng’s (1993) “news impact curves,” which plot the predicted volatility response implied by a model, against past price shocks of given sign and size.