Date of Award
Doctor of Philosophy
Dr. John Knight
Dr. Stephen Sapp
Dr. Martijn van Hasselt
My dissertation consists of four essays focusing on the estimation and forecasting of the discrete and continuous-time stochastic volatility (SV) models with volatility observable. The first essay examines the estimation of discrete-time SV models via a Monte Carlo study with both lagged inter-temporal and contemporaneous dependencies when volatility is observed. The statistical properties of both models are studied. Treating volatility as an observable variable, we apply traditional estimation methods including both full information maximum likelihood (FIML) and three-stage least squares (3SLS) methods. The estimation is straightforward and easy to implement. The Monte Carlo results suggest that both methods do a reasonable job at recovering the true parameters when the underlying volatility is observed. When the underlying volatility is unobserved, we should be careful in choosing an appropriate proxy such that the proxy error does not spread too much, and in this case, both FIML and 3SLS are able to provide good estimates. The second essay, which is closely related to the first essay, focuses on estimating and forecasting the discrete-time SV models with lagged inter-temporal and contemporaneous dependencies using realized volatility. This essay contributes to the literature in three aspects. First, we examine the estimation of the discrete-time SV models with lagged inter-temporal and contemporaneous
dependencies using realized volatility. Second, we investigate forecasting performance of discrete-time SV model with contemporaneous dependence. Third, we use realized volatility not only to evaluate the out-of-sample forecasting performance, but also in the in-sample estimation. The empirical results show that both FIML and 3SLS estimators produce good finite sample properties. The forecasting performances of four competing models, including SV models with lagged inter-temporal and contemporaneous dependencies, the simple regression model, and the heterogeneous autoregressive (HAR) model, are compared. In the third essay, we extend our study to examine the estimation via a Monte Carlo study of the affine continuous-time SV model when volatility is observed. Specifically, we apply the consistent approximate maximum likelihood method (C-AMLE). We simulate asset returns and volatilities at both daily and monthly frequencies. The Monte Carlo results suggest that the C- AMLE approach does a good job at recovering the true parameters. The fourth essay focuses on investigating the estimation of the affine continuoustime SV model using volatility proxies. Both realized volatility and model-free implied volatility are employed. We apply the C-AMLE approach as well as the quasi-maximum likelihood (QML) method. Our empirical analysis is based on both daily and monthly data of S & P 500 index and Dow Jones Industrial Average indexes. In general, the C-AMLE approach ourperforms the QML when the model-free implied volatility is used.
Xiao, Linlan, "ESTIMATION AND FORECASTING STOCHASTIC VOLATILITY MODELS WITH VOLATILITY OBSERVABLE" (2010). Digitized Theses. 3892.