Measurement Of Value At Risk Based On Ultra High Frequency Data

At present,financial institutions and investors mainly use Value-at-risk model to measure the market risk of asset portfolio.Existing research mainly adopts evenly spaced data to analysis volatility of stock price.because interval data is by means of sampling and interpolation on the basis of tick-by-tick data,that does not contain complete information.using tick-by-tick data can improve the integrity of data information.In this paper,we collecte tick-by-tick data of stock,applying Fourier method to estimate ultra-high-frequency volatility of stock,that is coupled with the GARCH model based on daily data to put forward the GARCH-UHFV model.The proposed model is inspired by the previous research which has put Realized Volatility(RV)in the GARCH model as the explanatory variable,named the GARCH-RV model.The biggest difference between the realized volatility and the ultra high frequency volatility is whether the data is evenly spaced or not.The realized volatility is based on high frequency data(e.g.5-minute data)which is evenly spaced,using the data to calculate the square of the yield as volatility.The ultra-high-frequency volatility is based on the unevenly spaced data,and Fourier analysis has the advantages of free model,unbiased and high stability.Due to the return sequence is not completely subordinate to the normal distribution,so this paper studies GARCH(1,1)model?GARCH(1,1)-RV model and GARCH(1,1)-UHFV model on the based of student t distribution to predict volatility and value at risk,and compared with the results on the based of normal distribution.There are two main conclusions :(1)It is true that the prediction accuracy of volatility can be improved by putting realized volatility to the variance equation of GARCH model,which is the same as reaserch of the earlier scholars.In addition,the GARCH-UHFV model can make up the hysteresis shortage of GARCH-RV model,and further improve the volatility prediction.(2)To some extent,the GARCH(1,1)-RV model can improve value at risk prediction.While GARCH(1,1)-UHFV model can make the prediction effect better.