Parameter Estimation Of Long Memory Stochastic Volatility Model Based On Moment Estimation Of Variation

The development of China's financial industry is still in its infancy,and there are many problems in the management of financial market.Therefore,it is complex and challenging to study the quantification of China's financial products,especially to estimate the parameters in the quantification model.Comte and renalut proposed a long memory fractional Brownian motion driven stochastic volatility model in 1993,and explored the estimation of parameters in the model.Because the volatility itself in the stochastic volatility model can not be observed directly,and the stochastic process driven by fractional Brownian motion does not have Markovian property,so it brings difficulties to parameter estimation.Many scholars have done research on this.Wang and Zhang(2014)and Wang Xiaohui(2015)improved the random volatility model driven by long memory fractional Brownian motion,and proposed a least-squares variation estimation method for the parameters of the model.However,this method is subject to the selection of the range m value,and there is no better range selection method,and the estimation effect is not stable.In this paper,we give another new estimation method for the model by using the square moment of variation,that is,the estimation method of the moment of variation.This method is relatively simple,the calculation speed is fast,and the estimation effect is better.Under the condition that Hurst index is known,the results of Monte Carlo simulation show that the moment of change estimation method can effectively estimate the unknown parameters ?,?.The estimation effect is good,the results are relatively stable,and the moment of change estimation is asymptotically normal.Finally,Monte Carlo simulation is used to compare the simulation results of the two methods.The results show that the proposed method has less volatility and more stable estimation.Under the condition that Hurst index is known,the results of Monte Carlo simulation show that the method of moment of change estimation can effectively estimate unknown parameters,the estimation effect is good,the results are relatively stable,and the estimation of moment of change is asymptotically normal.Finally,Monte Carlo simulation is used to compare the simulation results of the two methods.The results show that the proposed method has less volatility and more stable estimation.Finally,this paper makes an empirical analysis of the Shanghai Composite Index and Shenzhen Composite Index's 5-minute high-frequency data in recent two years,and concludes that the logarithmic return distribution of financial assets presents a peak thick tail phenomenon and the stock market in China has a long memory.At the same time,on the basis of the long memory random volatility model,the parameters are estimated and compared by using the moment of variation estimation method and the least square method,the results show that the moment of variation estimation proposed in this paper is better.