Modeling stock volatility with stochastic ARCH, GARCH and Stochastic Volatility model

Abstract

Modeling volatility within the log stock return is key to the stock price prediction. Despite numerous researches that modeled the volatility with conditional heavy-tailed error distributions, the unconditional distribution remains unknown. In this report, we use and follow the method introduced by Pitt and Walker (2005) by assigning a Student-t distribution for the marginal density of log return and constructing three models respectively, with similar structures to Autoregressive Conditional Heteroskedasticity (ARCH), Generalized ARCH (GARCH) and Stochastic Volatility model in a Bayesian way. We demonstrate the capability of the three models for stock price prediction with S&P 500 index and show that all our models outperform the standard GARCH model (Bollerslev, 1986).