Stochastic Autoregressive Volatility: A Framework for Volatility Modeling, Mathematical Finance
This paper introduces a general class of stochastic volatility models that can serve as a basis for modeling and estimating simultaneous equations systems involving multivariate volatility processes. The class consists of processes obtained as monotone polynomial transformations of so-called stochastic autoregressive volatility (SARV) models. The class permits a flexible modeling of volatility and avoids strong distributional assumptions. Most of the standard stochastic volatility models are incorporated in the framework, including the lognormal autoregressive model and stochastic volatility generalizations of GARCH and EGARCH. General conditions for strict stationarity, ergodicity, and the existence of finite lower-order unconditional moments for SARV are established. Closed-form expressions for the lower-order moments constitute the basis for the generalized method of moments estimation procedure. As an illustration, we consider and information-driven model of the return volatility-trading volume system for financial assets. Parameters with structural interpretation are estimated and an extended Kalman-filter procedure allows for the construction of volatility forecasts based on the bivariate return-volume series. Empirical results are based on daily NYSE data for IBM over 1973-1991.
Andersen, Torben. 1994. Stochastic Autoregressive Volatility: A Framework for Volatility Modeling. Mathematical Finance. 4(2): 75-102.