Study On Financial Market Volatility Models And Applications Via Fractal Theory

In recent years,a lot of empirical studies in the field of econophysics have shown that the price fluctuations exhibit obvious multifractal properties in financial markets.Through the study of multiscale analysis of financial markets,we can obtain different range of financial asset price fluctuation informations at different time scales(especially in the extreme cases),which provides a new way to explore the complexity of financial markets and risk management.By means of econophysics theories and methods,and under the framework of Fractal Market Theory,this thesis studies the fractal and multifractal characteristics of high frequency returns and realized volatility series in Chinese stock market,investigates multifractal volatility models and forecasts out-of-sample volatility,and apply the fractal and multifractal models to the study of stock index Futures hedging models.The main work and innovations of this paper are summarized as follows:1.This thesis improves the original MF-DMA algorithm,and exhibits the existences of fractal and multifractal properties in Chinese stock market.By adding the sliding window method,this thesis improves the MF-DMA algorithm which is used for the multifractal analysis of time series,in order to characteristic the multifractal properties of time series more accurately and comprehensively.Empirical investigations on several stock indexes and stock index futures show the existence of obvious long memory and multifractal characteristics of returns and realized volatility series in Chinese stock market,which state the applicability of the fractal and multifractal theory to the complexity research of Chinese stock market.2.This thesis proposes continuous multifractal volatility models based on products of stochastic processes under different distributions,and applies to realized volatility series of Chinese stock market.On the one hand,this thesis considers a multifractal model based on the products of stochastic process driven by log-normal distribution,and obtains the analytic expression of scaling function,empirical results verify the practicability and operability of the multifractal model to Chinese stock market.On the other hand,in order to better analyze the price volatility characteristics in financial market,this thesis compares the generalized multifractal models under different distributions by fitting to the realized volatility series in actual stock market.3.This thesis constructs a BMSM volatility model with skewed t innovations and forecasts the future volatility.The real financial asset return series exhibit non-Gaussian,with characteristics of leptokurtosis,fat tails and skewness.Therefore,this thesis constructs a BMSM-Skewed t model where the innovations are assumed to follow skewed t distribution in order to describe the characteristics of leptokurtosis,fat tails and skewness in returns series.This model is verified by the empirical analysis that it is superior to the traditional GARCH models on parameter estimation and future volatility forecasting.Besides,by using the skewed t innovations,the performance of data fitting and future volatility forecasting of this model is better than other BMSM models in the case of normal innovations and student's t innovations.4.This thesis studies hedging models via fractal market theory,proposes a stack-and-roll hedging model via fractal activity time and a Copula-BMSM dynamic hedging model.Assuming the underlying asset price model as FATGBM model based on the normal inverse Gaussian distribution,this thesis constructs the stack-and-roll hedging model via fractal activity time.The optimal hedging positions of stack-and-roll hedging at each stage are given by adopting the reverse induction.In the case of using CSI 300 index futures contracts to hedge the CSI 300 index spot,this model has very high risk hedging efficiency.This thesis also considers a dynamic Copula-BMSM hedging model by combining Copula function and multifractal volatility model.Empirical study shows that the hedging strategy derived by Copula-BMSM model involves less transaction costs than Copula-GARCH model,and Gaussian Copula-BMSM model has the highest hedging efficiency.