关键词: 价格极差, 已实现测度, CARR模型, 得分驱动模型, 乘性成分结构

Abstract:

Modelling and forecasting volatility is important for many financial applications， such as asset allocation， risk measurement and option pricing. It is well known that volatility is time-varying and highly persistent， and many models have been proposed to capture these stylized facts. The generalized autoregressive conditional heteroskedasticity （GARCH） model is among the most popular model. However， the model is return-based model that uses only daily closing prices to model and estimate volatility and fails to exploit the intraday information.An alternative approach for estimating volatility is to apply the daily price range， which is based on intraday high and low prices. The high-low price range has been proven to be a more efficient volatility estimator than the return-based one. The classical range volatility model， conditional autoregressive range （CARR） model， fails to exploits the intraday information in high-frequency data and belongs to the class of single component volatility models， which is incapable of capturing the dynamics of financial volatility adequately. An important feature of volatility is the high persistence （long memory property）. To account for this salient stylized fact of volatility， the additive component GARCH volatility models have been proposed in the earlier literature. In recent years， multiplicative component volatility models have received a great deal of attention in the financial econometrics literature. The models feature a multiplicative decomposition of volatility into a short-run and a long-run component. It is claimed that the multiplicative component models are more attractive than the additive component models， which are able to capture complex volatility dynamics such as the high persistence of volatility.By incorporating the realized measure， assuming a multiplicative component structure for the conditional range： the first component traces the long-run （secular） volatility trends， while the second component captures the short-run （transitory） movements in volatility， and adopting the score-driven approach to drive the dynamics of the two components， an extension of the CARR model is proposed， namely the score-driven multiplicative component realized CARR （SD-MCRCARR） model. The proposed SD-MCRCARR model that incorporates the realized measure （the intraday information of high-frequency data） as well as the multiplicative component volatility structure is able to quickly capture severe market fluctuation and to account for long-memory volatility. In addition， the model builds upon the score-driven framework which builds a dynamic update mechanism exploiting information contained in the score of the conditional distribution （predictive likelihood） of the observations. Also， an important advantage of the model is that the practical implementation of the model is simple since it is an observation-driven model and the likelihood function is available in closed form and therefore estimation can be easily performed by the maximum likelihood method.The empirical analysis using the high-frequency data of the Shanghai Stock Exchange Composite Index and Shenzhen Stock Exchange Component Index shows that the SD-MCRCARR model outperforms other benchmark models including the SD-CARR model， the SD-RCARR model and the SD-MCCARR model in the empirical fit. Further， the forecasting performance of the SD-MCRCARR model and the benchmark models are compared by using the robust loss functions and the model confidence set （MCS） test. The results show that the SD-MCRCARR model yields more accurate volatility forecasts than the benchmark models. Moreover， the superior forecast ability of the proposed SD-MCRCARR model is robust to alternative forecasting windows and forecasting horizons.

Key words: price range, realized measure, CARR model, score-driven model, multiplicative component structure