Forecasting Volatility Using Realized Stochastic Volatility Model With Time-varying Leverage Effect

The stock market is an important part of the macroeconomic market of all countries and the stock market volatility is very relevant to the economic situation,particularly in today's economic globalization and informationization.Due to the increasing degree of openness,the stock markets in various countries are affected not only by domestic speculation,economic conditions and policy direction,but also by foreign economic and political environment.Therefore,it is of great importance and practical significance to make accurate in-sample fitting and out-of-sample forecast of stock market volatility,and then make more effective portfolio decision,financial risk management and derivative pricing to reduce the market risk of financial assets such as stocks.Traditionally,for forecasting financial asset volatility more precise,there are mainly two types of models,the generalized autoregressive conditional heteroscedasticity(GARCH)model and stochastic volatility(SV)model,however,the forme rmodel assumptions for past volatility and the determination of return function,while the SV model assumes that it is a potential variables,through the introduction of an additional innovation process,the volatility model has more flexible structure and better performance.Moreover,on the one hand,with the improvement of communication level and information storage capacity,high-frequency data containing rich intraday information becomes more and more readily available in financial markets.The realized SV(RSV)model based on the realized volatility measure of high-frequency data has gradually replaced the traditional SV model.On the other hand,there have been sufficient studies on the constant leverage effect between volatility and return,but in recent years,more and more literatures have found that the leverage effect between return and volatility is time-varying.Therefore,on the basis of the traditional SV model and considering the realized volatility measure based on high-frequency data and the time-varying leverage effect between volatility and return,this paper constructs the time-varying leverage realized SV(RSV-TVL)model.Further,in order to accurately describe high persistence(long memory)of volatility,in order to further improve the prediction effect of RSV-TVL model in-sample and out-of-sample,based on the model,this paper decompresents the volatility multiplicative property into two components,namely,long-term and short-term,extended to the two factor RSV-TVL(2FRSV-TVL)model,and study whether the expanded model has better and more robust empirical performance.Taking the China's Shanghai Composite Index(SSEC)and Hang Seng Index(HSI),Japan's Nikkei 225 Index(N225),Korea's Composite Stock Price Index(KOSPI)daily high,low,opening,closing price and realized measurement(realized variance and realized kernel)based on 5 minutes of high-frequency data as samples,the newly constructed RSV-TVL model and the extended 2FRSV-TVL model are used for empirical research.First of all,time-varying leverage effect between return and volatility in the four index data is verified by the rolling time window method.Then,the RSV-TVL model,2FRSV-TVL model and five comparison models: the traditional SV model,leverage SV(SV-L)model,time-varying leverage SV(SV-TVL)model,RSV and leverage realized SV(RSV-L)model were respectively fitted in samples by using the maximum likelihood method based on a continuous fully adapted particle filter.Finally,the out-of-sample prediction performance of RSV-TVL model,2FRSV-TVL model and the above five comparison models were respectively studied based on the four loss function method,DM statistics method and MCS test method.The empirical results show that the introduction of the realized volatility measurement is significant for improving the out-of-sample prediction of the model.The introduction of constant leverage effect has a significant effect on the in-sample fitting of the model,but it is only when the out-of-sample prediction effect of the model is improved is combined with the realized volatility measurement.The introduction of time-varying leverage effect is significant for improving the in-sample fitting of the model,but it is significant for improving the out-of-sample prediction performance of the model only also by combining the realized volatility measure.Compared with the constant leverage effect,the time-varying leverage effect does not significantly improve the in-sample fitting effect of the model,but significantly improves the out-of-sample prediction performance of the model.The RSV-TVL model has better out-of-sample prediction effect than the RSV and SV-TVL)model.The 2FRSV-TVL model,which can significantly capture the high persistence characteristics of stock volatility,has better in-sample fitting and out-of-sample prediction performance than the RSV-TVL model.