In modern day financial risk management, modeling and forecasting stock return movements via their conditional volatilities, particularly predicting the Value at Risk (VaR), became increasingly more important for a healthy economical environment. In this dissertation, we evaluate and compare two main families of models for the conditional volatilities - GARCH and Stochastic Volatility (SV) - in terms of their VaR prediction performance of 5 major US stock indices. We calculate GARCH-type model parameters via Quasi Maximum Likelihood Estimation (QMLE) while for those of SV we employ MCMC with Ancillary Sufficient Interweaving Strategy. We use the forecast volatilities corresponding to each model to predict the VaR of the 5 indices. We test the predictive performances of the estimated models by a two-stage backtesting procedure and then compare them via the Lopez loss function. Results of this dissertation indicate that even though it is more computational demanding than GARCH-type models, SV dominates them in forecasting VaR. Since financial volatilities are moving together across assets and markets, it becomes apparent that modeling the volatilities in a multivariate framework of modeling is more appropriate. However, existing studies in the literature do not present compelling evidence for a strong preference between univariate and multivariate models. In this dissertation we also address the problem of forecasting portfolio VaR via multivariate GARCH models versus univariate GARCH models. We construct 3 portfolios with stock returns of 3 major US stock indices, 6 major banks and 6 major technical companies respectively. For each portfolio, we model the portfolio conditional covariances with GARCH, EGARCH and MGARCH-BEKK, MGARCH-DCC, and GO-GARCH models. For each estimated model, the forecast portfolio volatilities are further used to calculate (portfolio) VaR. The ability to capture the portfolio volatilities is evaluated by MAE and RMSE; the VaR prediction performance is tested through a two-stage backtesting procedure and compared in terms of the loss function. The results of our study indicate that even though MGARCH models are better in predicting the volatilities of some portfolios, GARCH models could perform as well as their multivariate (and computationally more demanding) counterparts. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2019. / April 2, 2019. / GARCH, MGARCH, SV, VaR / Includes bibliographical references. / Xufeng Niu, Professor Directing Dissertation; Giray Ökten, University Representative; Fred Huffer, Committee Member; Wei Wu, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_709859 |
| Contributors | Xiao, Jingyi (author), Niu, Xufeng (Professor Directing Dissertation), Ökten, Giray (University Representative), Wu, Wei (Committee Member), Huffer, Fred W. (Fred William) (Committee Member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Statistics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (91 pages), computer, application/pdf |
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