The Research Of Comparison Between Two Kinds Of Volatility Models

Since the 1970s in 20th century, with the macroeconomic environment changed, international and domestic financial markets had experienced profound transformation,financial market volatility and financial risks had increased clearly. It is important to understand and master the law and structure of fluctuations in the financial markets that how to measure the financial fluctuations, analyse and depict the characteristics of financial volatility. And the measurement and analysis of financial volatility must be realized through scientific methods and tools.Volatility, the uncertainty, is the core of researchment of modern financial theory.The uncertainty of the financial assets price can be measured through the variance of the proceeds of assets and the covariance between all kinds of the proceeds of assets. Back in the 1960s, it was recognized that variance and covariance were variational. But until the early 1990s, financial and monetary economic researchers only began to modeling the characteristics of variance of the first order matrix and the second order matrix. There are two kinds of models in describing the variational variance: autoregressive conditonal heteroscedasticity(ARCH) model and stochastic volatility(SV) model.They were released by Engle and Taylor in 1982 and 1986. This is the largest impact and one of the landmark work in the development process of financial metrology. I discuss the two models in my article deep.The major work done in my article systematically elaborating the background, statistical properties of autoregressive conditonal heteroscedasticity model communities and stochastic volatility model;deducting the generation of stochastic volatility model and relation between continuous stochastic volatility model and discrete stochastic volatility model through random differential equation. The result is that they are different types of the same random differential equation. And through random differential equation I acquired the inherent relations between autoregressive conditonal heteroscedasticity model and stochastic volatility model.