G-M Integrated Type Instantaneous Volatility Estimation For Stochastic Diffusion Model With Jumps

Volatility is an important feature of the financial market.It is directly related to the risk of the market and is an effective indicator of the quality and efficiency of the financial market.How to effectively reflect the dynamic behavior of financial market fluctuations through models has been a hot issue in financial market research.Especially when financial and economic fluctuations occur frequently,and the financial markets of various countries are globalized,It is of great theoretical and practical significance to further study the nature and regularity of volatility for financial risk prevention and evasion.In order to better change the asset price,the researchers added the jump com-ponent of price.For the jump-diffusion model,Barndorff-Nielson[1-3](2003,2006,2010)proposed the process of quadratic power variation and multiple power variation,and ob-tained a robust estimate of the integral volatility for jumping.Christensen and Posolskij[4](2005)combined with the idea of Barndorff-Nielson proposed a realized quadratic vari-ation process that is robust to jumps.Mancini[5,6](2004,2009)proposed the thresholdrealized volatility.When the price process includes jumps,Bandi and Nguyen[7](2003)and Johannes[8](2004)in Under the assumption that the jumping process has limited activity and is bounded,a kernel estimate of the diffusion function related to the price level is obtained.Inspired by these research literatures,in this paper,under the jump-diffusion mod-el,the GM-type kernel weight volatility estimation of the jump-diffusion model is con-structed using the second power variation.Under relatively weaker conditions,the es-timator of the estimator is weak.Consistency and asymptotic normality,and weak consistency of the nuclear power instantaneous volatility estimates,and gives the con-vergence rate.Finally,we investigated the finite sample nature of the estimator through numerical simulation studies.The numerical simulation results show that the estimator is an effective estimate of volatility when the jump is small,and the estimator is suitable for financial assets.The price has one or more small jumps.At this time,the estimated amount can effectively smooth the impact of the jump on the estimated value,and can be used as a reference for the risk fluctuation of the asset.However,when financial assets fluctuate violently,asset prices plunge sharply,or suddenly rise rapidly,the effect of this estimate may be limited.