A Study For The Smoothness Of Volatility Process In Chinese Stock Market

In this paragraph we discuss the smoothness of the volatility process in Chinese stock market.Conventional stochastic volatility models in which volatility are modeled as semi-martingales do not fit the empirical observations,especially the implied volatility surface.Gatheral shows that the rough volatility model which is driven by fractional Brownian motion with Hurst index H < 1/2 could produce reasonable consistence with market.On the basis of this theory,we alalysis the soothness property of Chinese stock market using the IF300 index time series.In this work,we firstly estimate the daily volatility of IF300 while choosing the proper realized measure.After that we use two statistical methods to calculate the H index of this series.we drive a conclusion that there is also an evident rough property in Chinese stock.This work lay the theory foundation for the Chinese options market and could be a good reference for the traders willing to use volatility strategy.This paper contains three chapters: In the first chapter,we mainly provide the bacground of this study and some new development of relative fields.In the second chapter,we provide a framework for the analysis of the uncertainty in the market.We also in this chapter discuss the connection between volatility and quadratic variation.In the follow chapter,we discuss the canonical estimator and the major fator causing the highly bias of this estimator:the microstructure noise.On the analysis of many estimators which all intend to get rid of the influence of microstructure noise,we choose two estimator to get the estimate volatility series of IF300 with the intraday data.In the end,we firstly analysis the fractional volatility model and the remarkable consistence with the empirical observations.The we use two statistical procedures to analyze the smoothness of the volatility series we get in last chapter and get the conclusion that the volatility of IF300 is also rough.