Nonlinear Financial Volatility Models And Their Empirical Research

High return and high risk appear simultaneously in financial markets. The risk in financial assets is usually measured by volatility in the modern finance theory. Volatility plays an important role in securities valuation, portfolio optimization, risk management, and hedge investment strategies. Therefore, it is popular for economists to estimate and forecast volatility. Under certain conditions, the traditional financial volatility models have been successfully used for forecasting volatility of assets return. To improve the forecasting accuracy of these models, in this study, grey forecasting theory, support vector machine theory and fuzzy inference technology are combined with the traditional financial volatility models, respectively. The main content of this dissertation is as follows:First, least squares support vector machine is applied to CARRX model and LSSVR based nonlinear CARRX model is established (LSSVR-CARRX). The empirical research on Hushen 300 index shows that LSSVR-CARRX model performs better than CARRX model in out-of-sample volatility forecasting. LSSVR-CARRX model captures the varying trend of range volatility better in long-term forecasting, and CARRX model has relatively accurate range volatility forecasts in short- and middle-term forecasting.Second, based on GM-GARCH type model, this study integrates SVRGM with GARCH model and Residual GM(1,1) model with EGARCH model, respectively, to reduce the stochastic and nonlinearity of the error term sequence. Empirical results indicate that SVRGM-GARCH model and RGM-EGARCH model outperform their benchmark models in forecasting volatility of Shenzhen stock index returns, respectively and are applicable to short-term volatility forecasting.Third, volatility is measured using range instead of return's standard deviation. Then grey support vector regression (GSVR) is applied to forecasting the volatility of Shenzhen fund market and v-SVR is the benchmark model. The empirical results indicate that GSVR could achieve better forecasting performance than v-SVR in shor-term volatility forecasting, while v-SVR has superior forecasting performance in long-term volatility forecasting.Fourth, TSK fuzzy model is applied to traditional GARCH type model. TSK based nonlinear GARCH model (TSK-GARCH) and TSK nonlinear combined forecasting model are established, respectively. The parameters and structure of TSK fuzzy model is determined by ANFIS. Empirical results indicate that TSK based volatility models provide better volatility forecasts than their benchmark models.In this study, grey forecasting theory, support vector machine theory and fuzzy inference technology are applied to the traditional financial volatility models and nonlinear financial volatility models are established. Empirical results on Chinese financial markets show that these theories and methods can improve out-of-sample forecasting performance of traditional financial volatility models. The study has important theory and practice value for modeling and forecasting of financial volatility models.