The Research On Return Jump Model Based On Realized Volatility

Empirical studies in recent years have shown that there are widespread jumps in the price of financial assets.And as an emerging market,the Chinese stock market is still relatively immature compared to other markets such as Europe and the United States,and jumps occur more frequently.Therefore,the study of jump behavior is conducive to better characterizing the statistical characteristics of the rate of return,which has important theoretical and practical significance for asset pricing,asset allocation,risk management and so on.This paper proposes a return jump model based on the realized variance and bipower variation measures developed by Barndorff-Nielsen and Shephard(2004,2006),and uses five-minute high-frequency data of the seven stock indexes in Chinese and American stock markets to conduct the empirical analysis.Motivated by Andersen et al.(2011),this paper models both jump sizes and jump occurrence.When modeling jump sizes,this paper extends the specification for squared jump sizes in Andersen et al.(2011)by deriving a simple conditional density for jump sizes with time-varying moments.Because the asymmetry of jump size density is modeled as a function of lagged realized variances,the conditional mean,variance,and skewness of jump sizes can evolve dynamically over time.When modeling jump occurrence,the ACH model was adopted in this paper.However,unlike Andersen et al.(2011),this paper prefers lagged realized variances as exogenous variables to model the conditional hazard rate for jumps in returns.After evaluating the model,this paper also analyzes the predictive power of the model.The empirical application of our model to equity indices demonstrates that asymmetry exists in the jump size density and that past realized volatility considerably affects both the jump size and jump occurrence.The performance of our model is statistically evaluated in terms of forecasting jump signs and the distribution density.The results demonstrate that compared with the benchmark ARMA(1,1)-GARCH(1,1)model,our model produces superior density forecasts for the jump size both in-sample and out-of-sample.And the model can provide accurate in-sample and out-of-sample probability forecasts for both jump occurrence and the jump signs.