The Comparison Study Of Parameters Estimation Of ARSV Model

The research on the financial market risk is one of the most interesting areas in financial study. The risk is mainly caused by the volatility of the price or returns. Therefore, the magnanimity and forecast of the volatility is the core problem in financial risk. Markowitz innovated measuring the volatility using mathematics concepts. He proposed measuring the volatility with sample variance. After him, a lot of models were proposed. Nevertheless, they all assumed the volatility as a constant. As the realization about the volatility, people know that the assumption of the volatility as a constant is improper. In 1980s, Autoregressive Conditionally Heteroscedastic(ARCH) models and Stochastic Volatility(SV) model were proposed.Stochastic Volatility model is one of the most important models in describing the volatility of financial market and its parameter estimation is a hot topic in this area. In this article, three estimation methods, GMM, MCMC and EMM are studied. GMM is one of the earliest methods used in SV model and its character is simple; MCMC is a Bayes analysis method which has developed in recent years for inference and prediction in SV model. The estimator of this method is more accurate than others. EMM is a relative new method for inference in SV model. Inference is sensitive to the choice of auxiliary model in small samples, but robust in larger samples.First, a brief introduction of SV model and a survey of its parameters estimation are given. Then, GMM, MCMC and EMM are described, including the theory, the application to SV model and the empirical study in our stock market. Last, a simple comparison of the three estimators is made.