Research And Application Of Volatility In Financial Data With Rounding Error

The modeling and prediction of volatility provide key information for the management of risk,the construction of investment portfolio and the pricing of derivatives.Volatility is an important indicator to describe the uncertainty of financial prices and measure risks.With the rapid development of modern economy and finance and the rapid change of market situation,it is inevitable to master the real-time information of volatility and study the volatility of high-frequency financial data.In practice,the data obtained is often obtained by rounding,and many studies often ignore the existence of rounding error.Most of the existing volatility literature only explores the impact of market microstructure noise.In fact,the impact of rounding error on volatility cannot be ignored,especially for high-frequency financial data.When there is rounding error,the traditional volatility can no longer be used as the consistent estimation of integral volatility,and can not be accurately estimated.Firstly,this paper proposes that rounding data is ubiquitous in practice,and ignoring rounding error will lead to a large deviation in volatility estimation.Based on the realized volatility（RV）,this paper focuses on the Two Scales Realized Volatility（TSRV）,the improved Two Scales Realized Volatility（TSRV₁）,and the corrected Realized Volatility（RV₁）proposed by Li and Mykland.By comparing the statistical properties of several volatility estimators and constructing their normal confidence intervals,and doing a lot of random simulation,the results show that the interval coverage ofRV₁ performs well.Secondly,the volatility estimator and its normal confidence interval were applied to the actual stock prices data,and it was also foundRV₁ to be more stable at different sampling intervals and less affected by rounding errors.In case analysis,the volatility estimator is biased and thick-tailed,and the normal confidence interval is no longer applicable.With the help of Edgeworth asymptotic expansion technique,the volatility with significant rounding error effect is studied,and the confidence interval of the improved volatility is constructed.Finally,a large number of random simulations and empirical analyses are performed on the improved confidence interval of Edgeworth.Compared with the traditional realized volatility estimator,the volatility estimator presented in this paper can better reflect the influence of the rounding error effect,and the validity of the confidence interval is improved to some extent by Edgeworth expansion.