Research On Modeling Of High Frequency Volatility Using Jump Intensity

In modern financial theory,financial asset returns and risk management are extremely important,and the estimation and forecasts of the volatility of financial asset returns is the most important.As an important and key indicator in the financial market,volatility plays an absolute role in asset portfolio optimization,derivative pricing and risk management.Therefore,the study of volatility is of great significance to the state,institutional investors and individual investors,and plays an important role in preventing risks.How to accurately measure and forecast volatility has also become the focus and hotspot of scholars.In the early days,scholars mainly used daily data or lower frequency data to model and forecast volatility,but there have been problems such as difficulty in parameter estimation,computational complexity and low precision.Based on the intraday high-frequency financial data,this paper uses the realized volatility(RV)estimator of the non-parametric method to measure the true volatility,so that the volatility can be directly observed and modeled,and the difficulty and complexity of parameter estimation of the model of forecasting volatility are reduced,and the scalability of the model is enhanced.Among all models,the heterogeneous autoregressive model(HAR-RV model)excels in the forecasts of realized volatility.Factors such as the impact of market information will lead to discontinuous jumps in the price of financial assets,and the research finds that the jump behavior contains useful information for the forecasts of volatility.Therefore,based on the intraday highfrequency data,we use ABD test and other non-parametric jump recognition methods to detect the existence of the jumps of the financial asset price process in the day;And we decompose the realized volatility into continuous volatility and jump volatility,and introduce them into the heterogeneous autoregressive model to construct the HAR-RVCJ model;Decomposing the realized volatility into positive and negative semivariations and introduce them into the model to construct the HAR-RV-CJ-RS model.Further?considering the second dimension of the jump behavior,the jump intensity contains useful information for forecasting the volatility.The Hawkes model is used to estimate the jump intensity,and the jump intensity is introduced into the model to extend the HAR-RV-CJ model and the HAR-RV-CJ-RS model.Furthermore,Considering that the median realized volatility(MedRV)measures the level of volatility of financial asset prices,which affects the probability of jump,MedRV is used as a marker to improve the Hawkes model to form a new Marked Hawkes model to reestimate jump intensity.Based on the new jump intensity,we improve the HAR model to obtain the new HAR-RV-CJ-MI model and the HAR-RV-CJ-RS model,and analyze the impact of the improved jump intensity on the realized volatility forecats.We choose two loss functions,the mean squared error and the logarithmic mean error squared,anduse MCS test and relative forecasting power test to evaluate whether the improved model's out-of-sample forecasting performance is improved,and select the best model.We use the high-frequency intraday data of S&P500 index as the research object.The empirical results show that the introduction of continuous volatility and jump volatility can improve the intra-sample forecasting performance and out-of-sample forecasting performance of the model;the realized positive and negative semi-variation has a significant contribution to the forecasts of realized volatility;the introduction of jump intensity as an explanatory variable can improve the prediction accuracy of the model,and the jump intensity estimated by the Marked Hawkes model is more effective than the jump intensity estimated by the Hawkes model.