"This paper shows that the stock market downturns of 2000-2002 and 2007-09 have very different proximate causes. The early 2000's saw a large increase in the discount rates applied to corporate profits by rational investors, while the late 2000's saw a decrease in rational expectations of future...

The stochastic volatility model usually incorporates asymmetric effects by introducing the negative correlation between the innovations in returns and volatility. In this paper, we propose a new asymmetric stochastic volatility model, based on the leverage and size effects. The model is a...