The Empirical Analysis Of Returns Volatility Based On Fat-tailed Distribution And Calendar Effect

The volatility of stock returns has important significance to the forecast of VaR and the investing of the investors. Therefore, it attracts the attentions of many scholars. At present,there are two kinds of models which can be used to describe the volatility of stock returns: one is ARCH (autoregressive conditional heteroscedasticity) models and another is SV (stochastic volatility) model. In this paper, we only use the ARCH models to characterize the volatility of stock returns. After considering calendar's effects on the mean equation and different distribution assumptions of residuals's effect on the variance equation fully, the author uses several ARCH models to analyze the volatility of the returns of shanghai composite which can most greatly reflect the stock market's volatility of China. After the demonstration analysis, we know that the return yield does not obey the normal distribution, and from the statistical characteristic pictures and QQ we see that the distribution of return yields with a thicker tail which is obviously larger than the normal-distribution. We add week virtual variables to mean equation and find the calendar effect exist in China's stock markets: The return in Monday,Wednesday is higher than in Tuesday and Thursday; After considering the calendar effects which has effect on the mean equation greatly, the equation which is based on the assumption of residuals normal distribution exists the lever effect while the equation of residuals based on t-distribution doesn't exist this lever effect. This means the conclusion of lever effect in China's stock market may comes from the inexactness assumption of residuals distribution. No matter we choose which model in ARCH, based on the information rules of AIC and SC, the simulation effect of t-distribution variance equation is much better than the normal-distribution equation.