The present work introduces three conditionally heteroscedastic models which allow an asymmetric reaction of the conditional volatility to the arrival of news. Such a reaction is induced by both the sign of past shocks and the size of past unexpected volatility. The three models are shown to converge in distribution to absolutely continuous Itô diffusion processes, as happens for other heteroscedastic formulations. Two out of the three proposed schemes differ from the existing asymmetric models, insofar as they are able to capture a particular aspect of the behaviour of the volatilities, i.e. the inversion of their asymmetric reaction to news. Empirical evidence from stock market returns in seven countries shows that Sign- and Volatility-Switching ARCH models outperform traditional asymmetric ARCH equations.
This paper builds on the initial ideas developed in 1994 work, "The Sign Conditional GARCH Model: Theory and Applications to International Stock Markets", Quaderni di Ricerca dell'Osservatorio e Centro di Studi Monetari, LUISS University, No. 41.
